This discussion clarifies the two definitions of entropy: statistical entropy and thermodynamic entropy. Statistical entropy, which pertains to randomness, is more general, while thermodynamic entropy relates to energy unavailable for work and is applicable primarily to systems near thermodynamic equilibrium. The relationship between these two forms of entropy is demonstrated through the Gibbs entropy formula, which aligns with the classical entropy formula under canonical ensemble conditions. This equivalence highlights the approximation of statistical entropy by thermodynamic entropy in equilibrium scenarios.
PREREQUISITESStudents and professionals in physics, particularly those studying thermodynamics and statistical mechanics, as well as researchers interested in the foundational concepts of entropy.
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.James Brown said: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?