# Why is entropy defined the way it is in classical thermodynamics?

Entropy as defined by the Clausius statement in classical thermodynamics, is only defined for equilibrium states.

I do not understand why is the definition restricted to equilibrium states. Would an unrestricted definition violate any of the axioms or laws of classical thermodynamics ?

An example would be really helpful.

• I think that on small time scales and non equilibrium states, the principle of entropy can locally be violated. So I think that the principle is actually only true for equilibrium states. Have a look at the Maxwell Demon Paradoxe Feb 21 '17 at 17:09
• I don't think non equilibrium states necessary require a microscopic definition. I am sure, we can have global parameters to describe a non equilibirum state of a system. Feb 26 '17 at 16:04
• How do you define a thermal equilibrium? Feb 26 '17 at 17:55

The entropy of a given macrostate is given as $S = k \log \Omega$, where $\Omega$ is the number of ways of rearranging the microstates of the system that give you the same macrostate. This is easy to define when you have a macrostate defined by parameters like $U, P, T, V$, etc. But thermodynamic state variables like that are only defined for equilibrium states.