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On E. T. Jaynes view, thermodynamic entropy of a system is, up to a multiplicative constant, the same as the the information entropy for the predicted distribution with maximum uncertainty conditioned on the expectation values of some state variables. In other words, thermodynamic entropy in a way has to do with the information we have about the system. If E. T. Jaynes Maximum entropy thermodynamics gives the correct explanation of entropy and the second law of thermodynamics, does a concept like "heat death" make any sense?

Gödel_vonNeum4nn
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    There is a conceptual jump at the end of this question. Why do you think there is a relation between heat death of the universe and the maximum entropy principle? – Mauricio Mar 13 '24 at 09:15
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    I think this is a good question and it sometimes pop up here in PSE. The point is that "entropy of the universe" is not a well-defined statement/quantity a priori, and hence all conclusions from it are too. – Tobias Fünke Mar 13 '24 at 09:46
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    @Gödel_vonNeum4nn As I said: before doing anything else, you have to argue that you can apply concepts of thermodynamics to the universe. Some critics to the "heat death" concept are summarized in the corresponding Wikipedia page. – Tobias Fünke Mar 13 '24 at 11:02

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Excellent profound question. Just my brief two cents here. I'm sure someone can elaborate better.

From a statistical mechanics point of view, the second law of thermodynamics (increase of entropy) emerges from course-graining phase space, i.e. loss of information. This is very consistent with the approach of Jaynes.

Indeed, suppose that at some point the universe reaches a complete thermodynamic equilibrium, which would be the most disordered, structureless case, then there would be no useful dynamics left to do, so one could call this a heat death.

Wouter
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Jaynes was just wrong. Thermodynamic systems change when they are out of equilibrium to get closer to equilibrium. This is a physical change in general. For example, if you have two pockets of gas at different pressure and temperature that come into contact their state will change physically as a result. This is definitely not a matter of anyone's knowledge since it can and does happen when nobody is around. For more explanation see "Time and Chance" by David Albert, Chapter Three, Section 3.

alanf
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    With all due respect, it seems you've not understood well the point of Jaynes. Your critic "This is definitely not a matter of anyone's knowledge since it can and does happen when nobody is around" does not apply and misses the point of Jaynes' formulation of statistical mechanics. For a good, yet critical discussion, see e.g. the book of Bricmont on stat. mech. – Tobias Fünke Mar 13 '24 at 10:58
  • To me Jaynes's interpretation is along the lines of Pippard, see quote here in which the entropy is tied to the constraints of the system. – hyportnex Mar 13 '24 at 13:27