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arXiv:1705.01750

Fluctuation Theorem for Arbitrary Quantum Bipartite Systems

Jung Jun Park, Sanguk Kim, Vlatko Vedral

Published May 4, 2017• 7 citations
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Abstract

We present a fluctuation theorem for quantum bipartite systems in which the subsystems exchange information with each other. Our information fluctuation theorem includes correlations by introducing a quantum mechanical mutual information content and a statistical probability distribution which allows one to consider statistical averages when computing the thermodynamic and informational quantities. The fundamental limit of heat transferred from a heat reservoir for quantum bipartite systems involving the quantum mutual information is then derived. We illustrate the use of our thermodynamic inequality in quantum computing and discuss our results in terms of Landauer's principle.

DOI
10.48550/arxiv.1705.01750

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We establish a fluctuation theorem for an open quantum bipartite system that explicitly manifests the role played by quantum correlation. Generally quantum correlations may substantially modify the universality of classical thermodynamic relations in composite systems. Our fluctuation theorem finds a non-equilibrium parameter of genuinely quantum nature that sheds light on the emerging quantum information thermodynamics. Specifically we show that the statistics of quantum correlation fluctuation obtained in a time-reversed process can provide a useful insight into addressing work and heat in the resulting thermodynamic evolution. We illustrate these quantum thermodynamic relations by two examples of quantum correlated systems.
Fluctuation theorems establish exact relations for nonequilibrium dynamics, profoundly advancing the field of stochastic thermodynamics. In this work, we extend quantum fluctuation theorems beyond the traditional thermodynamic framework to quantum multipartite information dynamics, where both the system and the environment are multipartite without assuming any thermodynamic constraints. Based on the two-point measurement scheme and the classical probability, we establish the fluctuation theorem for the dynamics of classical multipartite mutual information. By extending to quasiprobability, we derive quantum fluctuation theorems for multipartite coherence and quantum correlations, presenting them in both integral and detailed forms. Our theoretical results are illustrated and verified using three-qubit examples, and feasible experimental verification protocols are proposed. These findings uncover the statistical structure underlying the nonequilibrium quantum information dynamics, providing fundamental insights and alternative tools for advancing quantum technologies.
We investigate the link between information and thermodynamics embodied by Landauer's principle in the open dynamics of a multipartite quantum system. Such irreversible dynamics is described in terms of a collisional model with a finite temperature reservoir. We demonstrate that Landauer's principle holds, for such a configuration, in a form that involves the flow of heat dissipated into the environment and the rate of change of the entropy of the system. Quite remarkably, such a principle for heat and entropy power can be explicitly linked to the rate of creation of correlations among the elements of the multipartite system and, in turn, the non-Markovian nature of their reduced evolution. Such features are illustrated in two exemplary cases.
Two fundamental ingredients play a decisive role in the foundations of fluctuation relations-the principle of micro-reversibility and the fact that thermal equilibrium is described by Gibbs canonical ensemble. Here we investigate the statistics of heat exchange between quantum finite system coupled to two reservoirs at temperatures Th and Tc in the transient regime. We have obtained an analytical result for quantum heat fluctuation theorem in the transient regime. We consider a composite system consisting of two different heat baths at different temperatures with an intervening medium(system of interest). The system of interest is driven by an external protocol. For our study we invoke von Neumann two point projective measurement in quantum mechanics. Our result is a generalisation of Jarzynski-Wojcik heat fluctuation theorem.