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Thalion
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I've started studying statistical mechanics and thermodynamics on my own, and I'm confused about a few basic concepts. From what I can gather, the following two statements are true about a system in equilibrium:
1. A system is in equilibrium (by definition) when all of its micro-states are equally probable.
2. The entropy of a system is defined by the natural log of the number of micro-states available to the system.
The second claim can be used to show to that the entropy of a system increases when, for example, an energy constraint is removed that allows two subsystems to come into thermal contact, since the combined system has a greater number of available micro-states. Under this definition, it seems as if the entropy of a system in equilibrium is independent of the actual state of the system (and, in fact, that a system that is instantaneously in an odd state, say, all the gas in the corner of a room, can be in equilibrium provided this state occurs with the same frequency as all others).
How does this work with the idea of an individual state having a particular entropy? I have also seen references to the entropy of a state, defined as the natural log of the multiplicity of a particular state of the system, rather than the total number of states available to the system. Are these just two different types of entropy? It sometimes seems like books/articles are close to equivocating on the meaning of the word...
1. A system is in equilibrium (by definition) when all of its micro-states are equally probable.
2. The entropy of a system is defined by the natural log of the number of micro-states available to the system.
The second claim can be used to show to that the entropy of a system increases when, for example, an energy constraint is removed that allows two subsystems to come into thermal contact, since the combined system has a greater number of available micro-states. Under this definition, it seems as if the entropy of a system in equilibrium is independent of the actual state of the system (and, in fact, that a system that is instantaneously in an odd state, say, all the gas in the corner of a room, can be in equilibrium provided this state occurs with the same frequency as all others).
How does this work with the idea of an individual state having a particular entropy? I have also seen references to the entropy of a state, defined as the natural log of the multiplicity of a particular state of the system, rather than the total number of states available to the system. Are these just two different types of entropy? It sometimes seems like books/articles are close to equivocating on the meaning of the word...