Geometrical Excess Entropy Production in Nonequilibrium Quantum Systems
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. 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.
KeywordsNonequilibrium steady state Entropy production Clausius equality Geometrical phase Quantum Markovian master equation
The authors thank Keiji Saito for his helpful advice. This work was supported by a JSPS Research Fellowship for Young Scientists (No. 24-1112), a Grant-in-Aid for Research Activity Start-up (KAKENHI 11025807), and a Grant-in-Aid (KAKENHI 25287098). A part of this study was performed when TY and TS were in the Yukawa Institute for Theoretical Physics.
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