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  • We count symmetries of a system by counting the number of transformations/operations under which a feature of the system remains unchanged.
  • Entropy is a measure of the number of microstates that correspond to the observed macroscopic state (which remains unchanged when the change of microstates remain in a certain set, similar to the way symmetries work).

Is this a mere analogy or would it be possible to define entropy in terms of the concept of symmetry?

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@ali I'll take a feeble stab at this. First, this is my guess at what you mean.

Here is a "system" microstate 00110. Here is another "system" microstate 11000. Distinct microstates and the operation was roughly interchange places 3,4 and 1,2.

A system macrostate property is the sum over "places" for a given microstate. In this case both microstates have the macrostate property of 2. Conceptually, total entropy for this system is the number of ways I can get macrostate 2 out of rearrangements of the two 1's and 3 0's.

If we accept the definition provided for symmetry, then the symmetric "feature" is 2 and the symmetry "transformations" are the rearrangements of 1's and 0's. Within the context of this simple example, your question is justifiable but I sure don't know how far it goes. It only takes one counter-example to disprove any equivalence type of statement.

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  • $\begingroup$ Yes, this is a good illustrative example of what I meant. Do you think it is possible to extend examples like this to thermodynamic distinguishability, e.g. microstates as velocities and positions of particles and macrostates as measurements like temperature and pressure? $\endgroup$ – ali Mar 6 at 19:03
  • $\begingroup$ In thermodynamics, I guess a transformation would be any change in a microstate of particles without changing the macrostate of the gas. But would it be technically correct to talk about terms like "symmetries of a macrostate", or "increase/descrease in the number of symmetries" when the system's macrostate changes to another one with different number of microstates? $\endgroup$ – ali Mar 6 at 19:03

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