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Non-equilibrium Dynamics in the Quantum Brownian Oscillator and the Second Law of Thermodynamics

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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 (Kim and Mahler in Phys. Rev. E 81:011101, 2010, [1]).

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  1. Department of Physics, North Carolina A&T State University, Greensboro, NC, 27411, USA

    Ilki Kim

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  1. Ilki Kim
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Kim, I. Non-equilibrium Dynamics in the Quantum Brownian Oscillator and the Second Law of Thermodynamics. J Stat Phys 146, 217–238 (2012). https://doi.org/10.1007/s10955-011-0375-8

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  • DOI: https://doi.org/10.1007/s10955-011-0375-8

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