Non-equilibrium dynamics in the quantum Brownian oscillator and the second law of thermodynamics

Abstract

We initially prepare a quantum linear oscillator weakly coupled to a bath in equilibrium at an arbitrary temperature. We disturb this system by varying a Hamiltonian parameter of the coupled oscillator, namely, either its spring constant or mass according to an arbitrary but pre-determined protocol in order to perform external work on it. We then derive a closed expression for the reduced density operator of the coupled oscillator along this non-equilibrium process as well as the exact expression pertaining to the corresponding quasi-static process. This immediately allows us to analytically discuss the second law of thermodynamics for non-equilibrium processes. Then we derive a Clausius inequality and obtain its validity supporting the second law, as a consistent generalization of the Clausius equality valid for the quasi-static counterpart, introduced in [1].

Accepted for publication in Journal of Statistical Physics

References in corpus (6)

• Generalized Clausius inequality for nonequilibrium quantum processes
• Thermodynamics of a subensemble of a canonical ensemble
• Validity of Landauer's principle in the quantum regime
• Violation of the Zeroth Law of Thermodynamics in Systems with Negative Specific Heat
• The second law of thermodynamics in the quantum Brownian oscillator at an arbitrary temperature
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Cited by in corpus (1)

• Quantum thermodynamics from the nonequilibrium dynamics of open systems: energy, heat capacity and the third law