# Definition of equilibrium for thermodynamics and statistical mechanics

Is the definition of equilibrium for thermodynamics and statistical mechanics the same?

From my understanding, a system is in thermodynamic equilibrium if its macroscopic variables are not changing.

If we say a system is in equilibrium in statistical mechanics, what do we mean? What are the criteria the system has to satisfy?

• Simply saying that the macroscopic variables are not changing is not enough to say that a system is in thermodynamic equillibrium. You also need that there is no heat being transfered. A metal bar with its ends held at fixed temperatures and a constant flow of heat through it may be in a steady state, but it is not in thermodynamic equillibrium. – By Symmetry Dec 12 '18 at 13:53

The correct question to ask is "what are the criteria for equilibrium". The answer is:

the system is in equilibrium when temperature, pressure and chemical potential are constant and uniform throughout the system.

The answer is the same in both classical and statistical thermodynamics.