Timeline for If information-theoretic and thermodynamic entropy need not always be identical, which is more fundamental?
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Dec 6, 2020 at 17:45 | vote | accept | PrawwarP | ||
| Dec 5, 2020 at 19:17 | comment | added | warlock | @GiorgioP Boltzmann formula also was intended to use in connection with Boltzmann transport equation, which can be used for non-equilibrium gas. The slightly coarse-grained one-particle distribution in phase space ($μ$-space) can be used as a natural macrostate characterization for such gas. | |
| Dec 5, 2020 at 18:23 | comment | added | Christopher King | "In some cases, Information Theory may provide results consistent with thermodynamics, provided the interpretation rules of Thermodynamics have been used." That is a very good way to think about it. Information Theory, like any mathematical theory, only applies to the real world when given an interpretation. Even arithmetical facts are only true physically when used to model something that satisfies its axioms (like counting apples). | |
| Dec 5, 2020 at 18:17 | comment | added | GiorgioP-DoomsdayClockIsAt-90 | @warlock Boltzamnn formula was intended for use only in connection with microstates of an equilibrium isolated system. No generalization exists for generic non-equilibrium systems. What would be the characterization of the macrostate in such a case? | |
| Dec 5, 2020 at 18:06 | comment | added | warlock | There is well-established definition even when there is no local equlibrium. For classical (non-quantum) case it is Boltzmann's formula $\log N$, where $N$ is a count of microstates belong to current macrostate. Well, it may be some difficult to define macrostates in such cases, but this is another problem. | |
| Dec 5, 2020 at 17:47 | comment | added | GiorgioP-DoomsdayClockIsAt-90 | @warlock The so-called non-equilibrium entropy is connected to Local Thermodynamic Equilibrium conditions. Without that, there is no well-established definition of what a non-equilibrium entropy could be. | |
| Dec 5, 2020 at 17:44 | comment | added | warlock | In fact, thermodynamic entropy can be defined for nonequilibrium systems. Well, it may not be quetly correct to name it "thermodynamic" in this case, and it is better to say "physical entropy", but in general it is the same entropy. And it is possible, for example, to prove that the entropy of an equilibrium state is greater than the entropy of any nonequilibrium state. | |
| Dec 5, 2020 at 17:35 | history | answered | GiorgioP-DoomsdayClockIsAt-90 | CC BY-SA 4.0 |