Reconsideration of the generalized second law based on information geometry

Abstract

The maximum work formulation of the second law of thermodynamics has been generalized to transitions between nonequilibrium states. The generalization involves the relative entropy between nonequilibrium states and canonical states. The relative entropy scaled by the temperature of the canonical state quantifies the work available for extraction from the nonequilibrium state. This scaled relative entropy can be interpreted as an energy-dimensional divergence in information geometry. The generalized Pythagorean theorem relating three energy-scaled divergences, which we interpret as thermodynamic distances, gives a geometrical interpretation of the generalized maximum work formulation. Under this interpretation the optimal cyclic operation to extract work from a nonequilibrium state is discussed in a simple two-level quantum system.