Entropy, expanding space, Noether's theorem, and conservation of free energy
So here's a kinda-random thought that I don't really have anywhere better to discuss, and it's tangentially philosophical as much as any deep physics is, plus I know we have some pretty smart physicists here (@Kenosha Kid) who might be able to give some insightful replies:
The second law of thermodynamics (entropy always increases) only applies to closed systems.
By our current best understanding of physics, the universe as a whole is not a closed system, because there's new energy being created everywhere all the time by the expansion of space.
Per Noether's Theorem, conservation of energy is equivalent to time symmetry. Thus, that non-conservation of energy (the creation of new energy by expanding space) implies a time asymmetry.
The second law of thermodynamics is itself a time asymmetry.
So, could perhaps the second law of thermodynamics itself therefore be responsible for the creation of new energy via the expansion of space, which in turn undermines the effects of the second law on the universe as a whole?
As though the conserved quantity is not just energy per se, but free energy: so as some energy becomes unfree as entropy increases, there's a commensurate creation of new free energy to keep the total free energy constant, which new energy is added everywhere equally, manifesting as an expansion of space.
I'm not deeply studied enough in mathematics to figure out what the corresponding symmetry to conservation of free energy would be. Anyone care to follow up on this better than I can?
The second law of thermodynamics (entropy always increases) only applies to closed systems.
By our current best understanding of physics, the universe as a whole is not a closed system, because there's new energy being created everywhere all the time by the expansion of space.
Per Noether's Theorem, conservation of energy is equivalent to time symmetry. Thus, that non-conservation of energy (the creation of new energy by expanding space) implies a time asymmetry.
The second law of thermodynamics is itself a time asymmetry.
So, could perhaps the second law of thermodynamics itself therefore be responsible for the creation of new energy via the expansion of space, which in turn undermines the effects of the second law on the universe as a whole?
As though the conserved quantity is not just energy per se, but free energy: so as some energy becomes unfree as entropy increases, there's a commensurate creation of new free energy to keep the total free energy constant, which new energy is added everywhere equally, manifesting as an expansion of space.
I'm not deeply studied enough in mathematics to figure out what the corresponding symmetry to conservation of free energy would be. Anyone care to follow up on this better than I can?
Comments (54)
Quoting Pfhorrest
Yeah there's a few things you could be talking about here. There's dark energy which is thought to be driving the expansion of the universe, but also the ground state energy of all quantum fields in the universe. There's also the inflaton field, a dark energy contender, which expands space without reducing its energy density. Not telling you stuff you don't know, just thought I'd annotate your OP for the general readership
Quoting Pfhorrest
Noether's theorem isn't causal, it's more like two sides of the same coin. Here you're describing the expansion of spacetime necessitating a violation of conservation of energy. It wasn't just space that was created at the big bang but time too, and there's your time asymmetry necessitated by Noether's theorem.
This is very related to the second law though. If spacetime were fixed, the universe should tend toward equilibrium. But an expanding universe is constantly non-equilibrium: it's essentially creating more and more possible configurations of matter that are each more likely than the one we're in. There you do have a causal relationship: the expansion of space causes a thermodynamic arrow.
I hope that's useful. I'm not a cosmologist so maybe someone else out there will blow my mind.
I thought that according to the law of conservation of energy, that energy is neither created nor destroyed.
https://energyeducation.ca/encyclopedia/Law_of_conservation_of_energy
I looked this up on physics forum a few months back and some of their senior contributors were adamant that no new energy is created. I seem to think that such an idea would be very threatening on a foundational level.
I was thinking of dark energy, particularly the inflaton field. I'm a little unclear on the relationship between that and the ground state of quantum fields: is it not just making more space, all of which is filled with that ground level of energy, that accounts for the creation of new energy; or conversely, an increase in that ground level of energy that creates more space to contain it? (I guess since it's low-energy-density space that seems to expand, like the cosmic voids, that last thought doesn't make great sense).
Anyway, if I understand right through my sleep-addled brain, you're suggesting that it's not so much (as I was speculating) that maybe some law of preservation of free energy (/ some kind of equivalent symmetry) requires that more space and so energy be created to counteract the increase in entropy, but rather that the increase in space and so energy requires (or makes room for the possibility of) thermodynamic action to counteract the decrease in entropy. It's not things winding down that inflates space, but inflating space that keeps things wound up.
Quoting Wayfarer
On a local scale that is true, but on a cosmological scale it's not, because of dark energy, which is still a big mystery.
If eternal inflation theory is correct, the normal state of the infinite eternal universe is to be empty space that does nothing but create more empty space at breakneck speed, and the state of our universe as we know it is a "brief" "little" blip where that energy of the constant ongoing creation got dumped into a bunch of other fields instead of making new space; and the current acceleration of the expansion of the universe is our part of it gradually rejoining the rest of it in that normal state of breakneck expansion.
Yeah more or less. Thermodynamics is entirely reducible to statistical mechanics (which is in turn entirely reducible to quantum mechanics) which comes down to probability theory and combinatorics: if you imagine a partitioned box with gas in one partition and a vacuum in the other, when you remove the partition the gas expands to fill the whole box: you never get the gas collecting on one side or the other after a time. This is simply because the number of configurations of gas molecules that occupy the whole box greatly outweighs the total number of configurations occupying one side or the other (or the top, or bottom, or middle, etc.).
In the case of the inflaton field, expansion should be fastest where matter _isn't_, so as time goes on, we have more and more space to occupy, like a series of partitions being removed one after another, each giving access to a box that's exponentially larger than the last.
From https://en.wikipedia.org/wiki/Arrow_of_time
Just to add to what @Kenosha Kid said, entropy does not decrease when space expands. Rather, the ceiling of maximum entropy is lifted, so it has more room to grow. In the partitioned chamber example, before the partition was removed, each part of the chamber was at its maximum entropy. When the partition is removed, the configuration space is suddenly expanded, and so entropy can grow even further.
This is kind of how it looked 14 billion years ago, when the universe was a very uniform "particle soup." If not for expansion, it would've been at its maximum entropy already and nothing interesting would've happened.
I wasn't thinking that it did, but rather, that the creation of new energy that comes along with the expansion of space makes the universe an open system with a constant influx of new energy, which new energy can drive a reduction of entropy.
Not necessarily new. I'm not a physicist, but I am interested in the symmetry between Energy & Entropy. Apparently, the universe began with all the energy it would ever have. But energy is a shape-shifter, in that it is constantly changing form, from potential to kinetic, from energy to mass, and back again. The traditional list of energy forms -- chemical, electrical, radiant, mechanical, thermal and nuclear -- may need to be updated to accommodate "Dark Energy" and "Dark Matter". But the general rule seems to be : "conserve energy, because it doesn't grow on trees". Therefore, despite speculations about "continuous creation", or "exchanging energy between mini-verses in a multiverse, our world still remains a closed system. But it's a dynamic system, and cybernetic system. So, it's a slippery bar of soap, for physicists to pin down. :smile:
What is the source of energy that is accelerating space? :
[i]No new energy is created, it is potential energy converted into kinetic energy. ... The expansion is accelerating constantly, so that would seem to require a constant addition of energy. But if our universe is self contained, there is no external source of energy to create a force to accelerate space. . . .
There is no force or energy involved in the expansion of space. It is merely a natural result of the General Theory of Relativity.[/i]
https://www.researchgate.net/post/What-is-the-source-of-energy-that-is-accelerating-space
Enformy :
In the Enformationism theory, Enformy is a hypothetical, holistic, metaphysical, natural trend or force, that counteracts Entropy & Randomness to produce complexity & progress.
http://blog-glossary.enformationism.info/page8.html
Note -- (amateur guess) apparently, Enformy is symmetrical, in that it maintains a dynamic balance between Potential (stored) and Actual (kinetic) Energy, by cycling through various physical forms. As space expands, its potential energy is converted into kinetic or inertial energy. But the total (whole) energy content of the Cosmos remains the same as in the beginning, when it went Bang!.
In response to those thoughts I was mulling over what @Kenosha Kid was saying, about the enlargement of space making room for entropy to increase, and how it seems like the geometric arrow does drive the entropic arrow after all. I imagined to myself a little thought experiment or visualization: a toy system consisting of two points on a line segment, so it would have a very simple 2D configuration space, with obvious (err... note on that later*) peaks and valleys of entropy in it giving an obvious entropic arrow of time. And then, to that model, I added a third variable, and so a third dimension to its configuration space: the size of the line segment. Because higher-entropy states would be available on larger line segments, the entropic arrow of time would naturally point down the dimension of the configuration space that represents the size of the line segment...
...and I was about to say "regardless of what's going on with the entropy gradients along the other two dimensions", but that's not true, and not true in a very important way! It is true that even if there weren't those other two dimensions of the configuration space, like if there was just an empty line segment with nothing on it, there would still be an entropy gradient down the one-dimensional configuration space, corresponding to the size of the line. In other words, in a completely empty space, the entropic arrow of time will be toward a larger completely empty space. But if there's an even steeper entropy gradient in the other dimensions of the configuration space, thereabouts the entropic arrow of time will be angled further away from straight down the dimension of the configuration space representing a larger line segment: in other words, if there's any process that results in higher entropy faster than making more space, that will happen first.
So merely given that it's possible for space to expand, that there's not some law somehow preventing it, we should just statistically expect empty-enough space to expand merely because that's the fastest route to the most entropy, but if there are other faster routes to more entropy available, we should statistically expect to see those happen first before we see expanding space.
*Now for that note about the "very simple 2D configuration space, with obvious peaks and valleys of entropy". I was trying to visualize what that configuration space would look like, where the peaks and valleys of entropy would be, which states of that simple toy system are really more likely or less likely, and something occurred to me. There is exactly one state of the system where the two points are maximally far apart. There are increasingly more states of the system where the two points are increasingly closer together. The most common distance-apart for the two points to be, out of all the possible configurations of the system, is zero. That seemed counterintuitive to me: I initially expected that more-spread-out configurations would be more common, and I started trying to figure out where I had gone wrong. But upon reflection is occurred to me that on that counterintuitive account, we would statistically expect the two points to get closer and closer together... like gravity. And, if I'm not mistaken here, we would still expect more than two points to get more evenly distributed, but still for them to get closer together given a particular evenness of distribution.
In other words, on a purely statistical account, we would expect not just clouds of particles to even out, but also to fall together, and for the space surrounding them to get larger, in decreasing order... which is what happens IRL, no?
I know that there are already entropic accounts of gravity (though I don't know a lot about them), but I'm not sure if there are entropic accounts of the expansion of space yet?
Can you draw this? I'm struggling to see why a line on a 2D configuration space would be well-served by a third dimension representing the size of the line segment. My best interpretation is that you're introducing some non-locality but I'm not sure.
Quoting Pfhorrest
So entropy is essentially a count of the number of near-degenerate states (or microstates) that are equivalent (making a macro state). One way of increasing entropy therefore is to fix the number of particles and spread them out. But yeah there are other ways: increase the temperature, reduce the number of particles, stir the system up. These usually require work.
Quoting Pfhorrest
I'm not sure how you feel about that in light of the above. There may well be fewer macrostates where volume is maximised, but that doesn't mean fewer microstates. For two-particle systems this isn't necessarily important, since, on a line, there are really only a few microstates making up the macrostate of maximal separation (though I'm unclear why you think there is such a state). However for a macroscopic system, there are a huge number of such states, an exponential function of particle number. ({1, 2, 3, 4, ...}, {2, 1, 3, 4, ...}, {1, 3, 2, 4, ...} and so on.)
I can't really draw a 3D structure well enough, so I'll just try to elaborate.
Let's imagine you have a bitmap image one pixel tall and n pixels wide. All the pixels are black, except for two white ones, whose positions are variable. That's the system under consideration.
The configuration space for that system would have to be two-dimensional, because you have two free variables. You could depict it as an n-by-n image.
Then let's imagine a system just like that, except that n itself -- the width of the image -- is also variable. There's still only the two white pixels in it, whose positions are also variable.
For that you need a three-dimensional configuration space, because there are now three variables. That three-dimensional configuration space would be the stack of all of the various configuration spaces for the first type of system, with differing values of n.
Within each 2D slice of that 3D configuration space, you would have various gradients of the different degrees of entropy in each possible configuration of the system with some particular value of n. But there would be more and more high-entropy configurations within the 3D configuration space the further down the third dimension of the space you looked.
So overall, gradients of the different degrees of entropy in each possible configuration of the system will tend to run generally down that third dimension. If we define time as a path through the configuration space from less to more entropic configurations, then we would naturally expect the system to wind up with a larger value of n (a bigger image for our two pixels to move around in) over time. But if the entropy goes up faster just from moving one or the other pixel than it would by increasing the size of the image, we'd more likely see the pixels move around over time until that's no longer the case, and then the image will grow once that's the faster way to increase entropy.
Quoting Kenosha Kid
Stirring the system up sounds like it amounts to the same thing as spreading the particles around, but increasing temperature and reducing the number of particle both amount to creating or destroying energy (if we're talking about the system of the universe as a whole, I mean). That makes me wonder if, by the same principle I'm on about above, the only reason we see conservation of energy at all is because the quicker route to higher entropy involves moving energy around, and if the universe ever got to a point where there's almost no way to increase entropy by moving existing energy around, we might start to see violations of conservation of energy too. Although I don't see why there would be any expected trend for energy to increase or decrease monotonously, rather than back and forth in tiny intervals at random, so that might just amount to the existing microscopic quantum fluctuations of energy that we have anyway.
Quoting Kenosha Kid
I'm just talking about the toy system of points on a line. Let's look at our variation on that, the 1-by-n bitmap with two white pixels on a black background. For the sake of illustration let's set n=8 for now. There are exactly two (I mistakenly said one before) states where the white pixels are separated by 6 black pixels: if we call the pixels A and B and represent black space with underscores, those are the states:
A______B
B______A
But there's twice as many where they're only separated by 5 black pixels:
A_____B_
_A_____B
B_____A_
_B_____A
Six states where they're only separated by 4 black pixels:
A____B__
_A____B_
__A____B
B____A__
_B____A_
__B____A
And so on until there are fourteen states where A and B are adjacent. So over time (defined within the configuration space as above) we'd expect A and B to get closer to each other.
And then I was wondering if that could have any implications on gravity as a statistical phenomenon, although since I last posted I realized that perhaps this only works if the space in which the particles are located is finite, since there's equally-infinitely many ways for any two points on an infinite line to be separated by any finite distance... I think?
Okay, I get that. Thanks.
Quoting Pfhorrest
There's a bit more to it about making certain states accessible that otherwise wouldn't be, which is what I had in mind. I'm not sure it's relevant here though.
Quoting Pfhorrest
Like an expansion of space to allow entropy to increase, sure.
Quoting Pfhorrest
Yeah I got it, my point was that thermodynamics is a statistical concept. There are fewer microstates in the two-particle model for the maximal distance, so moving to it doesn't increase entropy, it would decrease it. However this only works in this this low-dimensional, low-particle-number model.
If we make this real and have two molecules in a tube, it would be very surprising to see each molecule at either end of the tube: that would be an ordered system. There's not really a concept of them filling the container.
As the number of particles increases, the number of microstates that fill the box increases exponentially and faster than the number of microstates that fill only part of the box and one approaches the limit where statistical behaviour is expected.
So I guess the question here is what is it you suspect thermodynamics fundamentally is when you're dealing with two particles in a tube? Because it can't be statistical and be demonstrated by your toy model*.
But all that aside, I like the idea that expansion is a kind of quantum tunnelling of the entire universe to a larger version of the universe to increase entropy. That does make some sense.
It may increase its energy, making the overlap between individual microstates and the current state vanishingly small, but if it increases the number of such microstates in compensation, it could still work.
*Actually it can be: even two-body systems are statistical in quantum mechanics (e.g. Pauli exclusion), just not in the sense of thermodynamics.
Again, I'm not qualified to comment on the mathematical or physical aspects of your proposed symmetrical relationship between Space & Time, or between Free Energy & Spatial Expansion. But, I am interested in the Philosophical and Cosmological implications of the proportional relationship between Energy and Entropy.
Noether's Theorem seems to be a special case of Maupertuis' Principle of Least Action. Which has been metaphorized as "The Lazy Universe Principle". But I would prefer to call it the "Conservative" or "Frugal Universe" principle. That is how I interpret the First Law. It's like Fossil Fuels : petroleum is not a renewable resource, so it must be used sparingly and recycled when possible. "A penny saved is a penny earned".
In this case, "Free Energy" is not free; it comes with a cost : Entropy (unavailable energy). So, the source of energy for the expansion of space is not a freebie. Therefore, the moral of this story is that Energy and Space-Time are finite --- hence, the expansion cannot go-on forever. :cool:
Maupertuis's principle :
It is a special case of the more generally stated principle of least action.
https://en.wikipedia.org/wiki/Maupertuis%27s_principle
The Lazy Universe :
https://aapt.scitation.org/doi/10.1119/1.5024210
Thermodynamic free energy :
Since free energy usually contains potential energy, it is not absolute but depends on the choice of a zero point. Therefore, only relative free energy values, or changes in free energy, are physically meaningful.
https://en.wikipedia.org/wiki/Thermodynamic_free_energy
The first law of thermodynamics states that energy can neither be created nor destroyed, only altered in form.
I'm not really sure; the stuff about gravity was an afterthought to the stuff about expansion, and if that part doesn't pan out, we can move past it.
If you know anything about Verlinde's entropic model of gravity though, I would be curious to hear how something like that might relate to this entropic model of expansion, if you'd care to pontificate on that.
Quoting Kenosha Kid
:up:
Quoting Gnomon
I don't see how you're getting that claim. I am both talking about the Principle of Least Action, and also talking about Noether's Theorem, but I don't see why you'd say one is a special case of the other.
The relationship between them that I'm talking about is: if the change that most efficiently increases entropy is for the universe to get bigger, then -- even though that makes a time asymmetry in the universe, and thus by Noether's theorem implies that energy is not conserved -- then that's what will happen. Or, conversely: that we only see energy conserved, even though it doesn't have to be, because there are more efficient means of increasing entropy ("lesser actions") available, and it isn't until all of those options are exhausted (such as in a gaping void of empty space) that we start to see the universe take advantage of other possibilities, like expanding space.
I don't, I'm afraid. The actual gravity is a function of temperature, I recall that, but I never got my head around why it's attractive. I'll try and squeeze in some pen and paper work on Sunday.
It wasn't exactly a "claim", but just an observation. I don't know much about either theory. But after reading descriptions, the "principle" seemed to be more general in application than the "theorem". In any case, I concluded that the PLA would have the opposite effect from "efficiently" Increasing Entropy. Instead, it would tend to conserve available Energy, acting as a brake on the dissipating effects of energy decay -- the end result of which is the projected Heat Death of the universe.
A more positive outlook is important to my philosophical worldview, including the hypothesis of Enformy (negentropy), which works in opposition to deconstructing & digressing Entropy. I had coined the term "enformy" before I had heard of "negentropy". And one reason that awkward word is not better known, may be that some misanthropic physicists appear to be less interested in positive evolution, than in the scary negative impact of the motor of the world running down, leaving us stranded in a bleak future, with nowhere to go. :grin:
Enformy :
In the Enformationism theory, Enformy is a hypothetical, holistic, metaphysical, natural trend or force, that counteracts Entropy & Randomness to produce complexity & progress.
http://blog-glossary.enformationism.info/page8.html
Negentropy is reverse entropy. It means things becoming more in order. By 'order' is meant organisation, structure and function: the opposite of randomness or chaos. One example of negentropy is a star system such as the Solar System. ... The opposite of entropy is negentropy.
https://simple.wikipedia.org/wiki/Negentropy
Addendum: imagine we begin the toy model earlier as a 1 pixel long 1 dimensional 1 bit depth image. That’s basically just a single bit, a 1 or 0, an empty set or a set containing the empty set. We’re allowed to make any changes to this that we like. We can change the one pixel from black to white. We can make the 1 dimensional image more pixels long. We can add dimensions to the image. We can increase the bit depth of the pixels. As the 1 dimensional 1 bit image is equivalent to an integer in binary, we can make whatever change that would make it into a rational or real instead. As multi-bit pixels are also basically integers, we can make them rationals or reals instead. Multi-channel (e.g. RGBA) pixels are basically matrices, so those can be matrices of reals if we want, and the whole image can then be a multidimensional (differentiable) manifold in which every point is a matrix of real or, hell why not, complex numbers. Or we can have an 11-dimensional image where every point is an octonion if we want instead. The important part is that we can get to that structure by gradually modifying our original structure that was basically a single bit.
And in principle, we could make a configuration space of all possible abstract structures. Including every possible configuration of whatever kind of structure turns out to be the perfect model of our universe. And then reckon time as a path of continuously increasing entropy through that configuration space.
In this way, all the very laws of the universe are merely local symmetries in that configuration space, things that the current chain of least actions don’t have reason to violate. But when violating them is the best route toward higher entropy, it’ll do that. And so a universe that began as literally just an empty set, a zero, one black pixel, evolved more dimensions, larger dimensions, and more and more complex structure, because that became the best way of increasing entropy. Our universe is currently… something like the cross product of several special unity groups… and doesn’t need to change from that in order to increase its entropy, because there are a lot of much more entropic structures of that sort it can cycle through before it has to resort to an altogether different kind of structure. But when it has to, it will. And it got to be this way in the first place because at various times in the past, it had to.
Good move! :cool:
I just came across the term "phantom energy" which seems to be what you are talking about. If such inflationary energy actually existed, it would result in a sudden "Big Rip", which sounds more dramatic (and unpleasant) than the current projection of a "Big Sigh" during the prolonged "heat death" of the universe. This reminds me of Woody Allen's quip : "I'm not afraid of death, I just don't want to be there when it happens". :joke:
Expanding Space -- Negative Gravity :
However… it is possible that our universe contains what is known as “phantom energy” in the literature. A universe with phantom energy is unstable, because the density of phantom energy is increasing when the universe expands, but just like dark energy, phantom energy accelerates expansion. But in this case, it becomes a runaway process, known as the “Big Rip”.
https://www.quora.com/What-if-space-expanded-so-fast-that-virtual-particle-pairs-were-pulled-away-from-each-too-quickly-for-them-to-annihilate-each-other/answer/Viktor-T-Toth-1?ch=99&share=a86bfb9b&srid=ozk3M
Phantom Energy :
Phantom energy is a hypothetical form of dark energy satisfying the equation of state with w < ? 1 {\displaystyle w<-1} w<-1. It possesses negative kinetic energy, and predicts expansion of the universe in excess of that predicted by a cosmological constant, which leads to a Big Rip. The idea of phantom energy is often dismissed, as it would suggest that the vacuum is unstable with negative mass particles bursting into existence. The concept is hence tied to emerging theories of a continuously-created negative mass dark fluid, in which the cosmological constant can vary as a function of time.
https://en.wikipedia.org/wiki/Phantom_energy
Big Rip :
https://en.wikipedia.org/wiki/Big_Rip
My personal cosmology is just the opposite of maximizing Entropy. Instead, the universe seems to be gradually maximizing order and organization. But, since we are currently at the You Are Here mid-point (in the graphic of my last post about the Big Rip), the amount of order right now is roughly equal to the amount of disorder.
However, if the "black pixel" was programmed to evolve in a positive (relative to humans) manner. That would imply that the original "set" (Singularity) was not "empty", but bursting full of Potential. If so, Evolution could be interpreted as the gradual actualization of that latent constructive Energy. Perhaps the destiny of this experiment in evolution would be something like a second Singularity -- as envisioned by Ray Kurzweil, or by Teilhard deChardin. :yum:
This makes no sense; in fact, it's contradictory. According to thermodynamics: order is DISorganization ... DISorder is organization. :chin:
Nope, just dark energy. Phantom energy is something on top of that, that may or may not exist. Dark energy definitely does.
I understand that you don't agree with my holistic & positive assessment of the direction of evolution. But how did you come-up with that Big Brother oxymoronic assertion? I assume you are thinking of Entropy as merely a mathematical description of the energy availability in a system. How can you equate "order" with "disorganization"? Is that how the world looks from a reductionist perspective?
In a non-mathematical sense (common sense), meaningful synonyms of Entropy are "disorder" and "disorganization". And in the context of describing the universe as an evolving system, dis-organization is the measurable effect of Entropy. A randomized system is not a system, because it lacks the patterns of organization that constitute a system. Entropy breaks down the order and organization of a functional system. That's why Claude Shannon defined "Information" in terms of Order (certainty ; meaning) versus Entropy (uncertainty ; meaningless). :cool:
Entropy as Disorder: History of a Misconception :
The claim “entropy is analogous to disorder” fails for one additional reason: the word “disorder” is hopelessly vague. Entropy is a precise, measurable quantity.
https://aapt.scitation.org/doi/10.1119/1.5126822
Entropy :
[i]1. a thermodynamic quantity representing the unavailability of a system's thermal energy for conversion into mechanical work, often interpreted as the degree of disorder or randomness in the system.
"the second law of thermodynamics says that entropy always increases with time"
2. lack of order or predictability; gradual decline into disorder.[/i]
___Oxford dictionary
Entropy :
In thermodynamics, entropy is often associated with the amount of order or disorder in a thermodynamic system.
https://en.wikipedia.org/wiki/Entropy_(order_and_disorder)
Systems Theory :
Some may view the contradiction of reductionism in conventional theory (which has as its subject a single part) as simply an example of changing assumptions. The emphasis with systems theory shifts from parts to the organization of parts, recognizing interactions of the parts as not static and constant but dynamic processes.
https://en.wikipedia.org/wiki/Systems_theory
Universe is an organized System :
A system is an entity with interrelated and interdependent parts; it is defined by its boundaries and is more than the sum of its parts (subsystem).
https://en.wikipedia.org/wiki/Systems_theory
Evolution, the argument goes, is a decrease of entropy, because it involves things getting more organized over time, while the second law says that things get more disordered over time. So evolution violates the second law. ...
http://physics.gmu.edu/~roerter/EvolutionEntropy.htm
[i]“War is peace.
Freedom is slavery.
Ignorance is strength.”[/i]
? George Orwell, 1984
Oh! I thought you were proposing some novel form of energy. :smile:
Just look in the mirror at the increasing disorder that's organizing you, Gnomon! From what you've written, it appears you profoundly misunderstand (or "metaphysically" deny) entropy. And btw, I'm not a "reductionist".
Again, you seem to be talking nonsense : "disorder that organizes". That paradoxical notion goes right over my pointy little head. It sounds like the "emptiness of space that is full of energy" in the quote below.
Can you explain "disorder that organizes" in dumbed-down terms for a simpleton like me. I'm sure you know more about such things that I do. However, since I'm neither a physicist nor a mathematician, I am not interested in the narrow technical details of Energy/Entropy. My concern is only in the broad general philosophical implications of such abstruse topics. If I really had a use for the arcane details, I would ask you to teach me.
But I can be satisfied with illustrative metaphors, such as "Entropy is the flip-side of Energy". And although they are discussed as-if they are physical substances, they are more akin to spiritual substances like ectoplasm. In that case, "Entropy is like the ghost of Energy past". Neither is a material substance, but merely a condition, a state -- like before and after. That's why mystified scientists use poetic terms like "Dark Energy" and "Dark Matter" and "Dynamic Fluid" as placeholders for real understanding.
Perhaps you are actually being poetic, and ironic, when you speak of "disorder that organizes". Are you just pulling my leg? Are you actually a holist, pretending to be a reductionist? Are you metaphysically equating destructive Entropy with constructive Energy to emphasize the paradox of all change : Life is merely the process of approaching Death. :joke:
Dark Energy, Dark Matter :
[i]"empty space" can possess its own energy. Because this energy is a property of space itself, it would not be diluted as space expands. . . .
The thing that is needed to decide between dark energy possibilities - a property of space, a new dynamic fluid, or a new theory of gravity - is more data, better data.[/i]
https://science.nasa.gov/astrophysics/focus-areas/what-is-dark-energy
“Exergy balance equation” :
There is a direct connection between exergy destruction, entropy generation, and the reference temperature of environment, namely Exd=T0?Sgen
https://www.sciencedirect.com/topics/engineering/exergy-balance-equation
Note -- the poetic expression of Entropy as-if it is generated as a positive product of expending available Energy (exergy), rather than another step on the slippery slope that leads to the Heat Death of the universe. :cool: .
Energy is the potential for positive change (work, construction, organization)
Entropy is the result of negative change (dissipation, destruction, disorganization)
Most of the discussion on this thread is beyond my pay level. But this struck me as odd.
Something being more likely than not depends on a comparison between prediction and actual. The LIKELIHOOD of anything happening is only meaningful from the stand point of human perception. Everything that happens has a certainly of 100% of happening, and our less than 100% perceptions of likelihood of things happening is due to our inability to calculate the future precisely.
Therefore the quoted paragraph is meaningless in the sense of physical reality, inasmuch as likelihood is a human concept only, and applicable only to human understanding.
Order is a human concept, much like likelihood of events to happen. Neither ought to be part of any physics concept, other than how they relate to human understanding.
Much like there is no perpetuum mobile in the macrophysical world, but every motion type is a perpetuum mobile in the microphysical world.
Maybe that's been debunked? I dunno.
SO: One last time: likelihood, chance, and probability are strictly human constructs, to fill gaps where we don't know the outcome, but have only statistical probability to predict. IN the real world, things happen only one way, and not many ways, so the chance of anything happening is 100%, not any less. Reality and events in reality are a straight path; there are no branches, and chance is an illusion. If you want branches, then reality ought to happen more than one way. But it does not, does it?
In quantum mechanics, entropy is basically the number of microstates -- exact and degenerate quantum states -- that make up a macroscopic state.
Doesn't it? Why would you think it didn't?
Anyway, the point of my explanation was to undermine your claim that probability is entirely a human construct. If there's only one possibility, the probability of that possibility being realized is 100%. If there are many possibilities, the probability of any particular one of them being realized is low. That's what alethic probability (rather than epistemic probability like you're talking about) is, definitionally: what percent of the various ways things could be are like so? That's the probability of things being like so.
Quoting Kenosha Kid
And so it goes from one microstate (minimum disorder, simplicity) to N microstates (maximum disorder, complexity) of a macrostate, no?
Because it's obvious it does not. Can you name two different events that happen to the same object at the same time and in the same respect? Can a car go forward and backward at the same time and in the same respect? Can an electron reverse its spin and keep the same spin at the same time and in the same respect? Can a decay to a nucleus happen and not happen at the same time and in the same respect, in a mass of nuclei of the same atom, where the nuclei decay in random order? My answer to my four questions is a resounding "no". If you say yes, a car CAN go both forward and backward at the same time and in the same respect, please demonstrate. Thanks.
I disagree. But that's okay. If you were right in your criticism, then the law of excluded middle would never be applicable. But it's always applicable. So your criticism fails.
You're probably aware of the idea of energy levels in quantum mechanics, often depicted as concentric orbits which is inaccurate but might do for now.
The higher the energy of an electron in an atom, the higher up these energy levels it is. Energy levels are labelled n=1,2,3,... In addition to these energy levels, for each value of n there are possible different angular momenta available, essentially the shape of the orbit in the concentric picture.
Those possible values are finite for finite n, and go L=0,1,2,...,n-1. In the absence of an external magnetic field, each of these orbit shapes have the same energy.
So for a hydrogen atom in its lowest-energy state (n=1), there is precisely one orbital shape: L=0. No angular momentum. Straight through the goddam middle. For the next highest energy level n=2, L=0 or 1: straight through the goddam middle or a tight orbit. For the next highest, L=0, 1 or 2: adding a slightly less tight orbit.
There are other parameters than L. There's spin S, and how L and S are coordinated, and these follow similar rules: for a higher energy level n, there are an increased number of possible values of these parameters. These are the electron shells you would have been taught in chemistry: 2, 8, 18, etc. that underpins the periodic table.
Thus as you add energy to a bound electron, you increase the number of equivalent states it could end up in, which is how entropy is defined in QM, from which you can derive statistical mechanics and its definition of entropy (and then thermodynamics and its version of entropy).
Thanks for the rest of the explanation, too. Yes, I remember from Grade 13 chemistry the bound electron paths, as they go 2, 8, 18, 32, ... 2*(n^2), where n is the cardinal number of the "shell", that is, a path that electrons take as the atomic number (the protons in the nucleus) dictate. Don't ask me why they take these shell structures... too many equations involved, but please do tell me the definition of entropy in QM. In my high school days the only electron path that had been found or calculated specific energy levels were the electron of the Hydrogen atom, which, as we all know, has only one electron. Exciting this electron could be calculated in those years to what L level it jumps to; maybe QM has advanced now to know and calculate the energy levels of other electron paths.
I think there are quite a number of post-graduate students or just other formal students of logic and philosophy on this site who take their previously learned knowledge and fail to apply it properly to new and emerging thoughts. Especially where pure reason is involved. I don't know why this has to be a problem, but the phenomenon of being over-learned and thus influenced to not understand simple explanations is certainly pervasive on this site.
Think about it again: I said that reality can't happen more than one way. To this your replied, "Doesn't it? Why would you think it didn't?" There is no historical evidence that something happened to anything anywhere at the same time and in the same respect both ways that contradict each other, and there is the a priori knowledge that something can't both happen and not happen at the same time and in the same respect. You are arguing against these, not against my argument that I derived from these two. You must first convince me that reality can happen more than one way, that is, to a specific body a specific event can happen and not happen at the same time and in the same respect.
I am sorry, but I close this discussion with you. If you don't see the point in the bolded part, then there is something fundamentally not in alignment in our thinking, and all further arguments would be futile. I don't like futile. It's a personal preference. Sorry.
S = k ln(W)
Entropy S is Boltzmann's constant k times the natural log of the number of microstates W.
Theoretically there is an infinite number of microstates. So entropy is a constant, and furthermore it is infinite.
Did you not want to write dW, that is, the change in microstates? And changing in which direction?
We'll get there yet.
Degenerate microstates for a particular macrostate.
Thank you. What is the unit of entropy in QM? This definition only yields a number. A number alone is not a physics value.
Boltzmann's constant has an SI unit of Joules (energy) per degree Kelvin (temperature), so entropy is the same. These are easily Googlable questions btw.
wonderful. Thanks. I shall turn my attention to google now, and ask it "What's the meaning of life", "What is the purpose of existence" and "who created the world, and what was he wearing at the time".