Elementary explanations of the second law of thermodynamics refer to probabilities of system states and seem convincing. But not when considering time-reversals, because the same statistical arguments should also apply there but they produce contradictions regarding entropy increases with time. (I think the difficulty is in whether or not the assumption of statistical randomness is appropriate because it depends on what is given and maybe also on the direction of time but I'm not an expert and this doesn't answer my question anyway.) While reading some literature about the direction of time I learned that the direction of time and the second law of thermodynamics all come from a very low entropy immediately after the big bang, with increasing entropy produced by things that include gravitational clumping (e.g., the formation of black holes and the merging of black holes to produce larger black holes). I learned that this is responsible for the second law of thermodynamics but it seems to me that this is an incredibly large-scale thing. Given this explanation it seems amazing to me that we can randomly select a tiny piece of matter (large enough to be macroscopic but tiny from the point of view of human perception) and find that it obeys the laws of thermodynamics. Is there an explanation of how such large influences on entropy (e.g., objects produced by gravity clumping) can produce a second law that is so incredibly homogeneous that we find the law obeyed by all of the tiny specs of material?
The law isn’t ``homogeneous", that just doesn’t make sense. I’d recommend https://www.google.com/url?sa=t&source=web&rct=j&opi=89978449&url=https://sites.ifi.unicamp.br/brum/files/2014/01/TimeArrow-Lebowitz.pdf&ved=2ahUKEwjxrIi3ke6DAxVOSaQEHVI5CaAQFnoECCAQAQ&usg=AOvVaw3rsNO20JSMFKd-ZfkRrf8d
which adresses precisely this question.
The resolution of the ``paradoxes" lies in properly defining the conditional probabilities.
Thank you Stam Nicolis. I need a little bit of time to carefully study the link you sent but a quick glance convinces me that I'm going to learn something from it. As with all RG threads that I have been involved with, you contribute a lot of insight. It amazes me that one person is able to have such a thorough understanding of so many different topics in both math and all branches of physics. You have my respect for that.
Glad to have been of help-it's always fun to test one's understanding... I'm just a physicist :)
Not able to answer these I’m afraid but just to make one comment.
There are many entropies. The Second Law refers to Clausius Entropy. This entropy is meaningful only at thermal equilibrium. since the universe is not at equilibrium, we cannot define a quAntity called the Clausius entropy of the whole universe.
it is widely assumed that the Boltzmann entropy is numerically equal to the Clausius Entropy. This is a theoretical assumption, since the BE can only be calculated for ideal gases. But even here, it is only at equilibrium that BE = CE. As the system evolves towards equilibrium, S=klnW is not the entropy of that system. The CE has no meaning out of equilibrium. This is understood by reminding ourselves that CE is a state function and so is independent of the route taken by the system to that state. On the other hand, W is dependent on the rate of equilibration, which can be controlled. it is only At equilibrium that W is independent of kinetics.
One should correct me if I’m wrong... The main question and answers provided in this topic are self-invalidating due to reasons below:
• Physically, homogeneity generally expresses a smooth distribution of matter strictly at the universe scale or above (it cannot be applied to a smaller kinda stuff as emphasized in the present topic)... And it shouldn’t be confused with a possible mathematical-homogeneity meaning the same degree for all terms of a given mathematical-expression of a so-said entropy.
• Logically, an isolated system cannot occur in a homogeneous universe where approximately 95% of all stuffs are said to be invisible and everywhere (the combination of so said dark energy and dark matter affecting both quantum and gravity everywhere)... And the notion of entropy should be worthless in modern physics since one can’t have a closed system in nature, consequently the so-called second law of thermodynamics shouldn’t even be called a law.
By homogeneous I meant that every tiny little spec of matter (tiny on a macroscopic scale but still macroscopic) would, if it was isolated from its environment to become an isolated system, obey the second law. If increasing entropy defines the arrow of time, the entropy of which piece of matter defines the arrow of time for me? The entire universe? Maybe there is enough homogeneity for the arrow of time to be the same everywhere?
Dear Edmonds, the property of homogeneity applies exceptionally for a universe considered as a whole, otherwise it is already known and proven thanks to the observation of nature that all other systems within the universe are not homogeneous (a galaxy, a solar system, a star, a planet, any emphasized hypothetical possible tiny little spec of matter at either a macroscopic or a microscopic scale ... are generally isotropic but not homogeneous)... So, what you meant is not physically conceivable.
Plus ''any attempt to isolate your suggested tiny little spec of matter is doomed to fail due to dark gravity'' ... So, before even talking about the entropy, the arrow of time and the so-called second law of thermodynamics, you first need a closed system which is not physically conceivable by the way.
I can see that I will be constantly criticized for using the word "homogeneous" in spite of explaining the intended meaning each time I used the word. So let me change the vocabulary. I mean the "sameness" of all the macroscopic pieces of matter in that their entropies will be nondecreasing if they become isolated from their environments. Also, thermodynamics was a very successful topic of physics before somebody decided that the theory is useless trash because of gravity. Gravity did not start today. We had gravity even during the days when the second law was demonstrated to be useful.
I think I have the answer after reading a paper from a link provided by Stam Nicolis . Assume there is some Hamiltonian description of particle physics, so Liouville's theorem applies and implies that the phase-space density is constant along a particle trajectory. Assume, also, that the conditions after the big bang were not only very low entropy but also a nearly uniform (in spatial dimensions) distribution of phase-space density. With an initial condition of a uniform density together with a constant density with time along any trajectory, we predict a uniform density everywhere for all times (incidentally, the equal a priori postulate of statistical mechanics comes from that). This explains the spatial uniformity in the arrow of time (i.e., every isolated macrosystem has a nondecreasing entropy).
Trying “to relate the so-called second law of thermodynamics (entropy= measure of a given increasing disorder) and homogeneity (uniform distribution)”, it’s like trying “to put and arrange things in a basket with at once both uniformity and disorder”... that’s simply not conceivable dear fellows.
Plus...It’s one thing to assume a given hypothesis is right... but it‘s another thing to prove it right in real world (the notion of big-bang is actually being demystified by the J.w.telescope and it is in contradiction with evidences).
Therefore, whatever the understanding of what might be the initial conditions, the only chance for a so-said early-universe to be considered as an isolated system “ would be to pop out of nothing“; unfortunately, it‘s illogical even to suggest something can get out of nothing... and we still end up with the same conclusion (a closed system is not conceivable in real world, the so-called laws of thermodynamics are overrated): “the main question and all answers in the present topic are self-invalidating”.
According to Olivier Hakizimana , "(a closed system is not conceivable in real world, the so-called laws of thermodynamics are overrated):" The laws of thermodynamics have done a good job of producing successful technology, so I would not trash it altogether as junk science. It is easy to criticize, not so easy to build. Fortunately, the pioneering scientists and engineers found ways to obtain useful conclusions in spite of all of the limitations of physical theories. This is done by searching for approximations that are still useful even when some complications are present but neglected (this is called modeling). This is how you build. If they did nothing but criticize, and complain about gravity, we would not know how to get the maximum efficiency from a steam engine (for example).
Anyway, I got the answer to my question so I'm not going to continue arguing with you about this. You can have the last word if you want about how wrong everything is (an easy criticism), it doesn't concern me.
In order to push boundaries and build something new (which should be the main gaol for any scientist), one must critically think and review the effectiveness of the work done by other scientists whoever they are (by doing so, we are not denigrating them)... so, when any said useful conclusion from a given pioneer is inconsistent with reality, it has to be addressed “no matter how controversial and difficult to handle” it may feel for the followers of the pioneer in question (approximately 100% of pioneers in thermodynamics were not aware of the fact that the visible universe represents approximately just 5% for their invincible laws to be neglected one day “to not say be trashed one day”).
That said, the present topic still self-invalidating.
I wasn't going to reply but I can't resist. You don't push any boundaries you just complain. That is the easy part. Complaining is easy. It is a necessary first step for improvements, but it is the easiest step. Fixing the theories and recognizing the conditions for which the old theories are still useful approximations is the build part. The build part is not so easy. You haven't done that part. You also don't give old theories credit for being useful approximations under appropriate conditions, you just complain as if they are completely useless. A good example is your claim that thermodynamics cannot be relevant because gravity implies that there are no isolated systems. So, old-school thermodynamics cannot ever accomplish anything? Really?
Excuse our frankness even if the topic didn’t go the way you expected (the main question and answers of the present topic are fundamentally still self-invalidating)... no one can fix anything by abiding blindly with the same old logic (no matter how fruitful it has been in the past, so sad).
When it comes to the build part, logic and empirical evidences count more than your emotions... testing new ideas in order to fix a theory does not always go the expected way, one must have an open mind and self-control over his emotions. You still have much to learn before even thinking about doing that part... hahahahaha.
OK, whatever you said. The readers can make up their own minds. I am done with this.