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phrased with a bit more depth and a bit less dependence on the verb "to be".
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CR Drost
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CorrespondingEntropy logarithmically measure of the number of microscopic states corresponding to some specific macroscopically-observable state, not the current macrostatesystem as a whole. The principle of entropy isPut another way: systems that ahave not yet found their equilibrium state, when left alone, increase their entropy. This would not be possible if the system seeks outhad the macro state that hassame entropy for all macrostates.

Indeed, the most microstates in it:driving principle of entropy in other words, ourmodern stat-mech says that we have some uncertainty about the underlying microscopic state of the system keeps multiplying and multiplying, until, withthat from a certain assumptionsperspective (basically, the one where every macroscopic quantity we cannot do much better than justcan determine is conserved) we can treat nature as simply choosing a microstate uniformly at random. (We have to tread carefully about what exactly uniformly means here but an “obvious” choice seems to replicate certain nice features, like that metals will have specific heats that look like $3R$ where $R$ is the gas constant—a result that I want to say is due to Einstein but I am not 100% sure.)

As a result of this principle of nature picking microstates at random, our equilibrium state is the macrostate which contains the most microstates, and our regression to equilibrium is a process of macrostates getting larger and larger.

Corresponding to the current macrostate. The principle of entropy is that a system seeks out the macro state that has the most microstates in it: in other words, our uncertainty about the underlying state of the system keeps multiplying and multiplying, until, with certain assumptions, we cannot do much better than just choosing a microstate uniformly at random.

Entropy logarithmically measure of the number of microscopic states corresponding to some specific macroscopically-observable state, not the system as a whole. Put another way: systems that have not yet found their equilibrium state, when left alone, increase their entropy. This would not be possible if the system had the same entropy for all macrostates.

Indeed, the driving principle of entropy in modern stat-mech says that we have some uncertainty about the underlying microscopic state of the system and that from a certain perspective (basically, the one where every macroscopic quantity we can determine is conserved) we can treat nature as simply choosing a microstate uniformly at random. (We have to tread carefully about what exactly uniformly means here but an “obvious” choice seems to replicate certain nice features, like that metals will have specific heats that look like $3R$ where $R$ is the gas constant—a result that I want to say is due to Einstein but I am not 100% sure.)

As a result of this principle of nature picking microstates at random, our equilibrium state is the macrostate which contains the most microstates, and our regression to equilibrium is a process of macrostates getting larger and larger.

Source Link
CR Drost
  • 39k
  • 3
  • 43
  • 116

Corresponding to the current macrostate. The principle of entropy is that a system seeks out the macro state that has the most microstates in it: in other words, our uncertainty about the underlying state of the system keeps multiplying and multiplying, until, with certain assumptions, we cannot do much better than just choosing a microstate uniformly at random.