Tatsuro Yuge, Takahiro Sagawa, Ayumu Sugita, Hisao Hayakawa
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 any scalar thermodynamic potential cannot be defined in terms of the excess heat for NESSs far from equilibrium, 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 there exists a scalar potential for the operation on a single reservoir in noninteracting systems, but that this is not valid in interacting systems.
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http://arxiv.org/abs/1305.5026
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