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In the definition of entropy, there are two. One is about the degree of randomness and one is about energy that is not available to do work. What is the relationship between them?
The former is statistical entropy and the latter is thermodynamic entropy. Statistical entropy is more general, while thermodynamic entropy is only defined for systems close to thermodynamic equilibrium. It can be shown (see the box in the link in the post above) that statistical entropy for systems close to thermodynamic equilibrium can be well approximated by thermodynamic entropy.In the definition of entropy, there are two. One is about the degree of randomness and one is about energy that is not available to do work. What is the relationship between them?