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arXiv:2402.06858 · Physical Review A

Evidence of genuine quantum effects in nonequilibrium entropy production via quantum photonics

Qing-Feng Xue, Xu-Cai Zhuang, Deyang Duan, Ying-Jie Zhang, Wei‐Bin Yan, Yunjie Xia, Rosario Lo Franco, Zhong‐Xiao Man

Published Oct 4, 2024• 2 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.110.042204

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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.
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.
Abstract The entropy produced when a quantum system at thermal equilibrium is driven to a non-equilibrium state can be considered as having components from coherence generation and from a population mismatch. The entropy component which is related to coherence represents a truly quantum effect and can be calculated using two different decompositions, based on either the relative entropy of coherence or on the thermal state corresponding to the Hamiltonian dephased in the eigen basis of the actual state. However, the decomposition based on the relative entropy was unable to quantify highly coherent processes or processes occurring in the low temperature regime. We experimentally explored a general driving scheme (a non-equilibrium process) on a nuclear magnetic resonance quantum processor, and were able to isolate the contribution of coherence to irreversible entropy generation. Furthermore, we numerically explored an infinitesimal driving process to distinguish between high and low temperature limits. The thermal equilibrium temperature and the final energy gap were varied to establish the relationship among temperature, energy level spacing, entropy production and coherence generation. Our results indicate that the contribution to entropy from coherence is higher in the low temperature regime. We also verified a generalized Clausius inequality, which affirms that the irreversible entropy production is lower-bounded.
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.
Exploiting the relative entropy of coherence, we isolate the coherent contribution in the energetics of a driven nonequilibrium quantum system. We prove that a division of the irreversible work can be made into a coherent and incoherent part. This provides an operational criterion for quantifying the coherent contribution in a generic nonequilibrium transformation on a closed quantum system. We then study such a contribution in two physical models of a driven qubit and kicked rotor. In addition, we also show that coherence generation is connected to the nonadiabaticity of a processes, for which it gives the dominant contribution for slow-enough transformations. The amount of generated coherence in the energy eigenbasis is equivalent to the change in diagonal entropy, and here we show that it fulfills a fluctuation theorem.
A central open question in quantum thermodynamics is the identification of thermodynamic entropy away from equilibrium. Although thermodynamic entropy coincides with the von Neumann entropy for a Gibbs state at equilibrium, the thermodynamic role of quantum coherence generated during nonequilibrium evolution remains unclear. Here, we show that von Neumann entropy does not, in general, represent the thermodynamic entropy governing heat exchange in coherent nonequilibrium quantum systems. By integrating the resource theory of quantum coherence with thermodynamic principles, we develop a general framework for nonequilibrium quantum thermodynamics. We identify thermodynamic entropy with the energy entropy derived from energy-measurement statistics and introduce a dynamical temperature extending the equilibrium concept to nonequilibrium states. Consequently, we obtain an exact entropy-balance relation separating the entropy flux associated with heat exchange from the coherence-loss contribution to entropy production, establishing an operational connection between quantum coherence, heat flow, and total entropy change. Unlike approaches relying on equilibrium reference states or stationary Gibbs ensembles, our framework uses instantaneous dynamical quantities and remains valid throughout transient nonequilibrium evolution. It provides consistent dynamical definitions of temperature, work, heat, and free energy. Applying the formalism to an exactly solvable open quantum system, we show that the first and second laws hold throughout transient evolution and that equilibrium thermodynamics emerges dynamically in the weak-coupling long-time limit. Our results establish a unified framework for coherent nonequilibrium quantum thermodynamics and suggest opportunities for controlling heat dissipation through coherence engineering in quantum thermal technologies.