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Journal of Mathematical Sciences

On the General Definition of the Production of Entropy in Open Markov Quantum Systems

Anton Sergeevich Trushechkin

Published Jul 29, 2019• 9 citations
Publisher
DOI
10.1007/s10958-019-04417-4

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The irreversible motion of an open quantum system can be represented through an ensemble of state vectors following a stochastic dynamics with piecewise deterministic paths. It is shown that this representation leads to a natural definition of the rate of quantum entropy production. The entropy production rate is expressed in terms of the von Neumann entropy and of the numbers of quantum jumps corresponding to the various decay channels of the open system. The proof of the positivity and of the convexity of the entropy production rate is given. Monte Carlo simulations of the stochastic dynamics of a driven qubit and of a $\ensuremath{\Lambda}$ configuration involving a dark state are performed in order to illustrate the general theory.
A quantum statistical expression for the entropy of a nonequilibrium system is defined so as to be consistent with Gibbs’ relation, and is shown to corresponds to dynamical variable by introducing analogous to the Heisenberg picture in quantum mechanics. The general relation between system-reservoir interactions and an entropy change operator in an open quantum system, relying just on the framework of statistical mechanics and the definition of von Neumann entropy. By using this formula, we can obtain the correct entropy production in the linear response framework. The present derivation of entropy production is directly based on the first principle of microscopic time-evolution, while the previous standard argument is due to the thermodynamic energy balance.