Complexity is orthogonal to entropy. The aforementioned barrier-separated box is high in entropy but simple. Upon lifting the barrier, a description of the gas front moving into the vacuum is enormously complex. It is also lower in entropy than the previous, barrier-separated state. Finally, when the gas is diffuse and entropy at its maximum, complexity dips back down.
Life is complex. Plants turn solar radiation into complex living structures; they also diffuse waste heat. Animals eat those plants, make more complex stuff, and generate more diffuse waste heat.
> The aforementioned barrier-separated box is high in entropy but simple.
This isn't true in any meaningful objective sense; representing the exact state of the system in some basis (e.g. the position or momentum states of all particles in the system) requires a huge amount of information, corresponding to the entropy. The GP only said it's a "simple" system because we (for arbitrary reasons) don't really care very much about the position of each gas molecule. We as humans are satisfied with describing the system in terms of bulk statistical characteristics like temperature and pressure. However, we would be unsatisfied doing the same thing with a similarly information-rich system such as a microprocessor, because now the bulk characteristics of the system aren't sufficient information to describe the characteristics that humans care about.
"Simplicity" or "complexity" as described by the GP is not a physical quantity; it's a reflection of which precise dynamical behavior we happen to care about. You could probably find all sorts of heuristics that generally match with human intuition, but in the end it's up to opinion.
As we know, the living stance can be maintained for only a relatively short time, after which it rapidly decomposes to background entropy.
Interesting to speculate, as living beings we are chock full of "micro-environments", there could be exceptions to the laws of nature as we've understood them that could account for certain mysteries of biological nature.
A living organism also increases the entropy of the environment.
Yes, but that's not what the person you replied to was saying. They were pointing out that there can be a global, absolute decrease in entropy, it's just statistically very unlikely.
What would you consider a "fundamental physical law"?
I'm surprised that Markov chains would be involved when the laws of physics are deterministic.
The Poincare recurrence theorem has always suggested to me that the second law is not as fundamental as other laws. For a finite system with finite phase space, the state of a system will traverse closed loops, repeating forever with no steady increase or decrease in entropy. (Edit: to be clear, I'm not claiming that what I just described is the Poincare recurrence theorem or that it applies to our universe. But it is worth considering systems where the second law doesn't apply and trying to figure out how and if they differ critically from reality.)
https://en.wikipedia.org/wiki/Poincar%C3%A9_recurrence_theor...
Not that my background is worth anything, but just so you know where I'm coming from, I have a PhD in physics, spent years thinking about the entropy of computation, and wrote parts of the Wikipedia entry on Maxwell's demon. I think much of the disagreement over entropy and the second law comes from how we frame the problem.
IIRC, the proof requires the markov chain be irreducible, and extends to the general case by summing over the irreducible parts; and that entropy will stay the same or increase while converging to the stationary distribution over states.
(Although it has now been 20 years since I dealt with these things so I might be misremembering. Time to retread Cover&Thomas I guess...)
[0] staff.ustc.edu.cn/~cgong821 /Wiley.Interscience.Elements.of.Information.Theory.Jul.2006.eBook-DDU.pdf seems to have a copy indexed by Google. I suspect it is not legitimate
Put another way: the second law of thermodynamics is not required to fully describe a universe that acts like ours appears to. It will "take care of itself" based on more fundamental descriptions of matter and its interactions.
I'm also comfortable with what appears to be fundamental today no longer being fundamental tomorrow.
The probability of either theory producing an incorrect prediction external to the theory is much higher, and will be about the same for each theory. That is, it's more likely we're wrong about all of physics than that the second law makes a bad prediction in a bulk system.
Explanation of "internal" vs "external" probability: http://lesswrong.com/lw/3be/confidence_levels_inside_and_out...
I did not remember the exact statement when I posted earlier, but here it is: the statement of the (markov) 2nd law of thermodynamics is also a statement about the sample space: It says that in expectation (over the ensemble) the relative entropy decreases towards that of stationary distribution (which in most systems is the highest entropy distribution possible in that system, thus absolute entropy is non decreasing). That is, unless the system starts at a state with a higher entropy than that of the stationary distribution, entropy will not decrease.
Both are mathematical statements, consequences of pure mathematics, neither of which gives a prediction - they both give ensemble averages, and both are both internally perfectly correct and consistent. See Cover & Thomas, 2nd Edition, Jul 2006, pg 81, section 4.4 - entropy rate of markov processes. Unless, of course, you are referring to a different version of the uncertainty principle which I am not familiar with.
Perhaps I have made the same mistake as you, and was thinking about the practical but non-generalized way the second law of thermodynamics is usually taught, which includes concepts like "the system will be in this state". The only part of your statement that is still probabilistic is "entropy will not decrease". That's not really true; it probably won't decrease.
>neither of which gives a prediction
"entropy will not decrease" is a prediction. It is possible (albeit overwhelmingly unlikely over large time scales) that this prediction is sometimes false.
The markov/IT version of the 2nd law is a statement about macrostate entropy (taking the entire microstate ensemble for each macrostate), and in that sense it is not probabilistic. See the Cover&Thomas reference I gave earlier for the exact definition. It is indeed different than how it is usually taught in physics, in which the microstates are differentiated.
I guess we both need to be more careful about mathematical definitions in the future ...
B. Was around at the beginning or prior to the big bang, as opposed to being the result of conditions early on.
C. What other laws, forces, constants, etc derive from.
I don't think enumerating the pedigree of a law gives it the seal of approval of validity. Newtonian physics also has pretty solid pedigree, and yet breaks down in relativistic conditions.
Please note I do not disagree with your conclusion, only with the way you present it.
https://www.amazon.com/Thermal-Physics-2nd-Charles-Kittel/dp...
Now play back time by looking at that particle's post collision path as the frame of reference and play time backwards. You will find a bias in input angles for these collisions.
In a microscopic level the physics can be time-symmetric (it seems not to be the case, there are T-symmetry violations), but macroscopically universe had higher entropy in the past (cosmological arrow of time)
edit: CPT-symmetry -> T-symmetry .
Kaon decay and B mesons decay break CP-symmetry and a CP-symmetry violation is equivalent T symmetry violation (CPT symmetry is preserved only if CP-violation is paired with T-symmetry violation)
This is because this idea is purely a tool to make calculations of large groups of particles as easy as one, but it does break down occasionally.
Newton's law of gravitation is stated in terms of a particle to particle relationship.
Center of Mass is the balance point of an object, and objects will always rotate around their center of mass unless constrained, but this doesn't relate to gravity.
You can approximate gravity at a distance from any object by using the object's center of mass, but that approximation breaks down when you're close to it.
The best way to prove this is to compute the gravitational force between your object and any arbitrary particle on the surface, then do the integration over all the particles (across the 3 dimensions).
Mass and energy is leaving, thus the average temp decreases but so does the particle count.
That said, it's entirely possible for entropy to spontaneously decrease in a closed system, the probability of this happening is just astronomically small for typical macroscopic systems.
Example:
If you have a system consisting of two compartments that are separated by a wall, where one of the compartments contains N particles. The system has low entropy because all the particles are on one side of it. Now, if you remove the barrier between the two compartments, particles will distribute evenly on both sides, increasing the entropy of the system. If we assume that the position of the particles is random, the probability of finding all of them on one side of the system is (1/2)^N, which quickly converges to zero for most macroscopic systems, which often contain > 10^23 particles.