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Quantum Science and Technology

Identifying contributions of classical and quantum correlations to entropy production in non-equilibrium quantum processes

Xu-Cai Zhuang, Qing-Feng Xue, Qi Zhang, Rui Huang, Yun‐Jie Xia, Zhong‐Xiao Man

Published Jul 10, 2025• 1 citation
Publisher

Abstract

Abstract Entropy production plays a pivotal role in characterizing the inherent irreversibility of non-equilibrium quantum processes, and a thorough understanding of this concept holds immense potential for advancing the design of thermodynamically efficient quantum technologies. In this work, we demonstrate that the entropy production observed in multipartite open quantum systems, undergoing independent dissipations, arises from two sources: the local dynamics governing individual subsystems and the non-local correlations embedded within the system. The contributions of quantum correlations, as genuine quantum effects, to entropy production are identified explicitly. The revelation of the source of entropy production is substantiated by an analysis of its stochastic counterpart, derived from quantum trajectories. Furthermore, we propose an experimentally feasible scheme to isolate the contributions of both classical and quantum correlations to entropy production. The theoretical findings are simulated using an optical setup. Our work establishes a profound connection between thermodynamic and informational quantities, elucidating the source of irreversibility in the non-equilibrium process of multipartite quantum systems and the genuine quantum contribution therein.

DOI
10.1088/2058-9565/adee41

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Abstract Entropy production plays a pivotal role in characterizing the inherent irreversibility of non-equilibrium quantum processes, and a thorough understanding of this concept holds immense potential for advancing the design of thermodynamically efficient quantum technologies. In this work, we demonstrate that the entropy production observed in multipartite open quantum systems, undergoing independent dissipations, arises from two sources: the local dynamics governing individual subsystems and the non-local correlations embedded within the system. The contributions of quantum correlations, as genuine quantum effects, to entropy production are identified explicitly. The revelation of the source of entropy production is substantiated by an analysis of its stochastic counterpart, derived from quantum trajectories. Furthermore, we propose an experimentally feasible scheme to isolate the contributions of both classical and quantum correlations to entropy production. The theoretical findings are simulated using an optical setup. Our work establishes a profound connection between thermodynamic and informational quantities, elucidating the source of irreversibility in the non-equilibrium process of multipartite quantum systems and the genuine quantum contribution therein.
Abstract Thermodynamic irreversibility is well characterized by the entropy production arising from non-equilibrium quantum processes. We show that the entropy production of a quantum system undergoing open-system dynamics can be formally split into a term that only depends on population unbalances, and one that is underpinned by quantum coherences. This allows us to identify a genuine quantum contribution to the entropy production in non-equilibrium quantum processes. We discuss how these features emerge both in Lindblad-Davies differential maps and finite maps subject to the constraints of thermal operations. We also show how this separation naturally leads to two independent entropic conservation laws for the global system-environment dynamics, one referring to the redistribution of populations between system and environment and the other describing how the coherence initially present in the system is distributed into local coherences in the environment and non-local coherences in the system-environment state. Finally, we discuss how the processing of quantum coherences and the incompatibility of non-commuting measurements leads to fundamental limitations in the description of quantum trajectories and fluctuation theorems.
Entropy production is a fundamental concept that plays a crucial role in the second law of thermodynamics and the measure of irreversibility. It imposes rigorous constraints on the kinds of transformations allowed in thermodynamic processes. Using an optical setup, here we experimentally demonstrate the division of entropy production of an open quantum system into a population-related component and a coherence-related component, supporting previous theoretical predictions. The coherence-related component represents a genuine quantum contribution with no classical counterpart. By adjusting bath temperatures and initial coherences of the system, we first derive the total entropy production due to both populations and coherences, then remove all the coherences of the system to solely obtain the population-related contribution. The difference between these two results permits to isolate the coherence-related term. Based on this division, our experiment ultimately provides proof of principle that irreversibility at the quantum level can be reduced through properly harnessing the two contributions to entropy production.
Thermodynamics is a phenomenological theory describing the energy conversion of work and heat. At its origins thermodynamics was developed in order to understand and improve heat engines. In conventional thermodynamics, however, only such processes are completely describable which are slow enough to keep the system of interest in an equilibrium state with its thermal environment at all times. On the contrary, all real physical processes are accompanied by non-equilibrium phenomena. These are mathematically described with the help of the irreversible entropy production, i.e. the dissipated work divided by the temperature of the bath. The second law of thermodynamics merely states that the irreversible entropy production is on average always positive. The modern trend of miniaturization, however, leads to smaller and smaller devices. On short length scales thermal noise as well as quantum fluctuations become important. Thus, usual thermodynamic quantities as work and heat acquire stochastic nature. Moreover, in the quantum regime a completely new theory had to be invented, since classical notions of work and heat are no longer valid. The present dissertation contributes to this prevailing field by the derivation of analytical expressions for the entropy production in open and closed quantum system far from thermal equilibrium. The theoretical treatment is motivated by an experimental point of view. The obtained results were derived from the reduced dynamics of the quantum mechanical system, which may be coupled to a thermal bath. To this end, it was dealt with methods and approaches of statistical physics, conventional thermodynamics, quantum information theory and the theory of open quantum systems. In this dissertation the most important physical systems are treated. First, an isolated system is considered before later on a heat bath is included. The limit of weak as well as of strong coupling are analyzed in detail. For isolated systems it turns out that a geometric approach is able to capture the thermodynamic properties, completely. To this end, the irreversible entropy production is sharply estimated from below by the angle between the real non-equilibrium state and the corresponding equilibrium one. Further, it is shown that the Heisenberg uncertainty relation for energy and time can be formulated more precisely in terms of that angle. As experimental system cold ion traps are introduced, in which the theoretical predictions can be verified. For weakly coupled systems, then, the irreversible entropy production is identified and a fluctuation theorem is derived by merely thermodynamic arguments. As experimental system we, again, propose the cold ion traps, where the heat bath can be simulated with the help of LASER light. In the limit of strong coupling a semiclassical description of the reduced quantum system is discussed. Again, an analytically exact expression for the entropy production and the corresponding fluctuation theorem is derived. A physical system, in which strong coupling to the environment can be analyzed, is given by Josephson junctions. This dissertation discusses the entropy production for isolated, weakly coupled, and overdamped quantum systems. For these physical regimes analytical relation are derived and experimental systems proposed, with which the predictions can be verified.
Entropy production quantifies the amount of irreversibility of a physical process, leading to fundamental bounds for thermodynamic quantities. It captures the inability to run a physical system forward and then backward, bringing it to the same initial state. Considerable research has been carried out in the last decades to extend entropy production to non-equilibrium quantum processes. We experimentally investigate the entropy production of such forward-backward cycles affected by genuinely quantum irreversibility. Namely, we consider processes realized to erase different types of correlations between two interacting systems, from obliterating solely quantum coherence to completely decorrelating local states. This makes the measurement of entropy production experimentally challenging. Addressing this challenge is the purpose of this paper.
Abstract One of the major goals of quantum thermodynamics is the characterization of irreversibility and its consequences in quantum processes. Here, we discuss how entropy production provides a quantification of the irreversibility in open quantum systems through the quantum fluctuation theorem. We start by introducing a two-time quantum measurement scheme, in which the dynamical evolution between the measurements is described by a completely positive, trace-preserving (CPTP) quantum map (forward process). By inverting the measurement scheme and applying the time-reversed version of the quantum map, we can study how this backward process differs from the forward one. When the CPTP map is unital, we show that the stochastic quantum entropy production is a function only of the probabilities to get the initial measurement outcomes in correspondence of the forward and backward processes. For bipartite open quantum systems we also prove that the mean value of the stochastic quantum entropy production is sub-additive with respect to the bipartition (except for product states). Hence, we find a method to detect correlations between the subsystems. Our main result is the proposal of an efficient protocol to determine and reconstruct the characteristic functions of the stochastic entropy production for each subsystem. This procedure enables to reconstruct even others thermodynamical quantities, such as the work distribution of the composite system and the corresponding internal energy. Efficiency and possible extensions of the protocol are also discussed. Finally, we show how our findings might be experimentally tested by exploiting the state of-the-art trapped-ion platforms.
Abstract We report on the experimental quantification of the contribution to non-equilibrium entropy production stemming from the quantum coherence content in the initial state of a qubit exposed to both coherent driving and dissipation. Our experimental demonstration builds on the exquisite experimental control of the spin state of a nitrogen-vacancy defect in diamond and is underpinned, theoretically, by the formulation of a generalized fluctuation theorem designed to track the effects of quantum coherence. Our results provide significant evidence of the possibility to pinpoint the genuinely quantum mechanical contributions to the thermodynamics of non-equilibrium quantum processes in an open quantum systems scenario.