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arXiv:1309.6586 · Physics Reports

The resource theory of informational nonequilibrium in thermodynamics

Gilad Gour, Markus P. Müller, Varun Narasimhachar, Robert W. Spekkens, Nicole Yunger Halpern

Published May 11, 2015• 401 citations
arXivHTMLPDF
DOI
10.1016/j.physrep.2015.04.003

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The field of quantum resource theory (QRT) has emerged as an invaluable framework for the examination of small and strongly correlated quantum systems, surpassing the boundaries imposed by traditional statistical treatments. The fundamental objective of general QRTs is to characterize these systems by precisely quantifying the level of control attainable to an experimenter. In this review article, we refrain from providing an exhaustive summary of the extensive literature on QRT. Rather, our focus centers on a specific subliterature founded upon the theory of majorization. The primary aim is to augment our comprehension of genuine quantum phenomena manifested across diverse technological applications and incite investigations into novel resource theories encompassing multiple types of resources. Consequently, we emphasize the underlying similarities shared by various resources, including bipartite quantum entanglement, quantum coherence, and superposition, alongside informational, thermal, and generalized nonequilibrium resources.
For classical discrete systems under constant composition (specifically substitutional alloys), canonical average acts as a map from a set of many-body interatomic interactions to a set of configuration in thermodynamic equilibrium, which is generally nonlinear. In terms of the configurational geometry (i.e., information about configurational density of states), the nonlinearity has been measured as special vector on configuration space, which is extended to Kullback-Leibler (KL) divergence on statistical manifold. Although they successfully provide new insight into how the geometry of lattice characterizes the nonlinearity, their application is essentially restricted to thermodynamic equilibrium. Based on the resource theory (especially, thermo-majorization), we here extend the applicability of the nonlinearity to nonequilibrium states obtained through single-shot work on Gibbs state. We reveal that the extended nonlinearity for nonequilibrium state is bounded from upper and lower by the information about one of the optimal Renyi divergences for equilibrium states in between practical and linear systems, and temperature and work.