Time-reversal symmetry relations for currents in quantum and stochastic nonequilibrium systems

TL;DR

This paper reviews recent developments in nonequilibrium quantum statistical mechanics, focusing on time-reversal symmetry relations that extend classical response theories and their applications in quantum transport.

Contribution

It presents new symmetry relations in quantum systems driven out of equilibrium, generalizing classical response formulas beyond linear response.

Findings

Derived generalized fluctuation relations for quantum systems.

Extended Kubo and Casimir-Onsager relations beyond linear response.

Applied symmetry relations to quantum transport in mesoscopic circuits.

Abstract

An overview is given of recent advances in the nonequilibrium statistical mechanics of quantum systems and, especially, of time-reversal symmetry relations that have been discovered in this context. The systems considered are driven out of equilibrium by time-dependent forces or by coupling to large reservoirs of particles and energy. The symmetry relations are established for the exchange of energy and particles between the subsystem and its environment. These results have important consequences. In particular, generalizations of the Kubo formula and the Casimir-Onsager reciprocity relations can be deduced beyond linear response properties. Applications to electron quantum transport in mesoscopic semiconducting circuits are discussed.