Geometrical Excess Entropy Production in Nonequilibrium Quantum Systems

TL;DR

This paper extends the concept of Clausius equality to nonequilibrium quantum systems, deriving a geometrical expression for excess entropy production that involves a vector potential, with implications for thermodynamics of nonequilibrium steady states.

Contribution

It introduces a geometrical framework for excess entropy production in quantum Markovian systems, highlighting the role of vector potentials in nonequilibrium thermodynamics.

Findings

Derived a geometrical expression analogous to Berry phase for excess entropy production.

Showed the reduction to the extended Clausius equality in the weakly nonequilibrium regime.

Demonstrated the existence of scalar potentials in non-interacting systems but not in interacting ones.

Abstract

For open systems described by the quantum Markovian master equation, we study a possible extension of the Clausius equality to quasistatic operations between nonequilibrium steady states (NESSs). We investigate the excess heat divided by temperature (i.e., excess entropy production) which is transferred into the system during the operations. We derive a geometrical expression for the excess entropy production, which is analogous to the Berry phase in unitary evolution. Our result implies that in general one cannot define a scalar potential whose difference coincides with the excess entropy production in a thermodynamic process, and that a vector potential plays a crucial role in the thermodynamics for NESSs. In the weakly nonequilibrium regime, we show that the geometrical expression reduces to the extended Clausius equality derived by Saito and Tasaki (J. Stat. Phys. {\bf 145}, 1275 (2011)). As an example, we investigate a spinless electron system in quantum dots. We find that one can define a scalar potential when the parameters of only one of the reservoirs are modified in a non-interacting system, but this is no longer the case for an interacting system.