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arXiv:2507.01602 · Physical Review A

Fluctuation theorems for multipartite quantum coherence and correlation dynamics

Kun Zhang, Mo-Yang Ni, Hailong Shi, Xiao-Hui Wang, Jin Wang

Published Feb 4, 2026• 0 citations
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Abstract

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.

DOI
10.1103/sgmk-bdjy

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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 derive detailed and integral quantum fluctuation theorems for heat exchange in a quantum correlated bipartite thermal system using the framework of dynamic Bayesian networks. Contrary to the usual two-projective-measurement scheme that is known to destroy quantum features, these fluctuation relations fully capture quantum correlations and quantum coherence at arbitrary times. We further obtain individual integral fluctuation theorems for classical and quantum correlations, as well as for local and global quantum coherences.
Fluctuation theorems are fundamental extensions of the second law of thermodynamics for small systems. Their general validity arbitrarily far from equilibrium makes them invaluable in nonequilibrium physics. So far, experimental studies of quantum fluctuation relations do not account for quantum correlations and quantum coherence, two essential quantum properties. We here experimentally verify detailed and integral fully quantum fluctuation theorems for heat exchange using two quantum-correlated thermal spins-1/2 in a nuclear magnetic resonance setup. We confirm, in particular, individual integral fluctuation relations for quantum correlations and quantum coherence, as well as for the sum of all quantum contributions. These refined formulations of the second law are important for the investigation of fully quantum features in nonequilibrium thermodynamics.
We study an arbitrary nonequilibrium dynamics of a quantum bipartite system coupled to a reservoir. For its characterization, we present a fluctuation theorem (FT) that explicitly addresses the quantum correlation of subsystems during the thermodynamic evolution. To our aim, we designate the local and the global states altogether in the time-forward and the time-reversed transition probabilities. In view of the two-point measurement scheme, only the global states are subject to measurements whereas the local states are used only as an augmented information on the composite system. We specifically derive a FT in such a form that relates the entropy production of local systems in the time-forward transition to the change of quantum correlation in the time-reversed transition. This also leads to a useful thermodynamic inequality and we illustrate its advantage by an example of an isothermal process on Werner states.
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 provide universal constraints on nonequilibrium energy and entropy fluctuations, making them a natural framework to assess how and to what extent quantum resources become thermodynamically relevant. We develop a unified framework for incorporating a generic quantum resource, including athermality, quantum coherence, and entanglement, into fluctuation theorems. We work within the end point measurement scheme, which avoids an initial energy measurement and allows quantum resources in the initial state to affect nonequilibrium energy statistics. We derive a family of quantum fluctuation theorems, including generalized Jarzynski equalities and Crooks type fluctuation relations, in which corrections decompose into resource resolved contributions. For single systems, we introduce the concept of weight of athermality, and combine it with the weight of coherence to isolate distinct thermodynamic effects of these quantum resources. For bipartite systems, we furthermore obtain two families of entanglement-resolved fluctuation theorems using an appended correlation operator and the best separable approximation, respectively. Finally, we introduce the concepts of coherence and entanglement fluctuation distances, as Kullback Leibler divergences, which quantify the thermodynamic relevance of quantum resources in a process-dependent and operational manner.
We analyze the production of entropy along nonequilibrium processes in quantum systems coupled to generic environments.First, we show that the entropy production due to final measurements and the loss of correlations obeys a fluctuation theorem in detailed and integral forms.Second, we discuss the decomposition of the entropy production into two positive contributions, adiabatic and nonadiabatic, based on the existence of invariant states of the local dynamics.Fluctuation theorems for both contributions hold only for evolutions verifying a specific condition of quantum origin.We illustrate our results with three relevant examples of quantum thermodynamic processes far from equilibrium.