Quantum thermodynamics of the Caldeira-Leggett model with non-equilibrium Gaussian reservoirs

TL;DR

This paper extends the Caldeira-Leggett quantum model to non-equilibrium reservoirs with squeezed and displaced thermal modes, enabling the study of quantum thermodynamics under engineered non-equilibrium conditions.

Contribution

It introduces a versatile non-equilibrium model with engineered reservoirs, develops a full heat statistics framework, and explores thermodynamic symmetries and quantum-classical correspondence.

Findings

Reservoir engineering induces effective time dependence and pure work sources.

Fluctuation theorem for energy balance is established.

Quantum-classical correspondence links heat statistics to classical Langevin dynamics.

Abstract

We introduce a non-equilibrium version of the Caldeira-Leggett model in which a quantum particle is strongly coupled to a set of engineered reservoirs. The reservoirs are composed by collections of squeezed and displaced thermal modes, in contrast to the standard case in which the modes are assumed to be at equilibrium. The model proves to be very versatile. Strongly displaced/squeezed reservoirs can be used to generate an effective time dependence in the system Hamiltonian and can be identified as sources of pure work. In the case of squeezing, the time dependence is stochastic and breaks the fluctuation-dissipation relation, this can be reconciled with the second law of thermodynamics by correctly accounting for the energy used to generate the initial non-equilibrium conditions. To go beyond the average description and compute the full heat statistics, we treat squeezing and displacement as generalized Hamiltonians on a modified Keldysh contour. As an application of this technique, we show the quantum-classical correspondence between the heat statistics in the non-equilibrium Caldeira-Leggett model and the statistics of a classical Langevin particle under the action of squeezed and displaced colored noises. Finally, we discuss thermodynamic symmetries of the heat generating function, proving a fluctuation theorem for the energy balance and showing that the conservation of energy at the trajectory level emerges in the classical limit.