Geometrical Excess Entropy Production in Nonequilibrium Quantum Systems

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.

28 pages, 3 figures. 'Remark on the fluctuation theorem' has been revised in ver. 2. Brief Summary has been added in Sec. 1 in ver. 3

References in corpus (5)

• Generalized Clausius inequality for nonequilibrium quantum processes
• Modeling heat transport through completely positive maps
• The geometry of thermodynamic control
• Steady State Thermodynamics for Heat Conduction -- Microscopic Derivation
• Geometrical Pumping in Quantum Transport: Quantum Master Equation Approach

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