Non-linear Onsager relations for Gaussian quantum maps

Abstract

Onsager's relations allow one to express the second law of thermodynamics in terms of the underlying associated currents. These relations, however, are usually valid only close to equilibrium. Using a quantum phase space formulation of the second law, we show that open bosonic Gaussian systems also obey a set of Onsager relations, valid arbitrarily far from equilibrium. These relations, however, are found to be given by a more complex non-linear function, which reduces to the usual quadratic form close to equilibrium. This non-linearity implies that far from equilibrium, there exists a fundamental asymmetry between entropy flow from system to bath and vice-versa. The ramifications of this for applications in driven-dissipative quantum optical setups are also discussed.

6 pages

References in corpus (7)

• Creating and probing macroscoping entanglement with light
• The Wigner Entropy Production Rate
• Quantum jumps and entropy production
• Non-equilibrium quantum chains under multi-site Lindblad baths
• Entropy production in linear Langevin systems
• Wigner entropy production and heat transport in linear quantum lattices
• Quantum thermodynamics of two bosonic systems

Cited by in corpus (5)

• Lyapunov equation in open quantum systems and non-Hermitian physics
• Upper bound for quantum entropy production from entropy flux
• Irreversible Entropy Production rate in a parametrically driven-dissipative System: The Role of Self-Correlation between Noncommuting Observables
• Quantum Onsager relations
• Casimir-Onsager matrix for weakly driven processes