Finite-bath corrections to the second law of thermodynamics

Understand

The second law of thermodynamics states that a system in contact with a heat bath can undergo a transformation if and only if its free energy decreases.

• However, the "if" part of this statement is only true when the effective heat bath is infinite.
• In this article we remove this idealization and derive corrections to the second law in the case where the bath has a finite size, or equivalently finite heat capacity.
• This can also be translated to processes lasting a finite time, and we show that thermodynamical reversibility is lost in this regime.