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Physical Review A

Effects of one-way correlations on thermodynamics of a multipartite open quantum system

Qi Zhang, Yun‐Jie Xia, Zhong‐Xiao Man

Published Dec 13, 2023• 8 citations
Publisher

Abstract

In this study we investigate how correlations of a multipartite quantum system affect its thermodynamics when subsystems of which interact with a thermal reservoir in a cascaded manner. We propose the concept of apparent temperature for an individual subsystem, which is determined by one-way correlations of the subsystem with its preceding subsystems and governs the direction of heat flow between the subsystem and reservoir. We demonstrate the possibility of reversing heat flow between the subsystem and reservoir conditioned on the apparent temperature and derive the conditions for achieving this reversal. We also examine the entropy production of this thermodynamic process and observe a tradeoff between contributions from one-way and global correlations to entropy production. Our results provide insight into the roles of one-way multipartite correlations on thermodynamic properties and expand the ways of applications of quantum resources in the area of thermodynamics.

DOI
10.1103/physreva.108.062211

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In this study we investigate how correlations of a multipartite quantum system affect its thermodynamics when subsystems of which interact with a thermal reservoir in a cascaded manner. We propose the concept of apparent temperature for an individual subsystem, which is determined by one-way correlations of the subsystem with its preceding subsystems and governs the direction of heat flow between the subsystem and reservoir. We demonstrate the possibility of reversing heat flow between the subsystem and reservoir conditioned on the apparent temperature and derive the conditions for achieving this reversal. We also examine the entropy production of this thermodynamic process and observe a tradeoff between contributions from one-way and global correlations to entropy production. Our results provide insight into the roles of one-way multipartite correlations on thermodynamic properties and expand the ways of applications of quantum resources in the area of thermodynamics.
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.
The second law of thermodynamics dictates that heat flows spontaneously from a high-temperature entity to a lower-temperature one. Yet, recent advances have demonstrated that quantum correlations between a system and its thermal environment can induce a reversal of heat flow, challenging classical thermodynamic expectations. Here, we experimentally demonstrate that internal quantum coherence in a multipartite spin system can also reverse heat flow, without relying on initial correlations with the environment. Under the collision model with cascade interaction, we verify that both the strength and the phase of the coherence term determine the direction and magnitude of energy transfer. These results enable precise control of heat flow using only local quantum properties.
The second law of thermodynamics dictates that heat flows spontaneously from a high-temperature entity to a lower-temperature one. Yet, recent advances have demonstrated that quantum correlations between a system and its thermal environment can induce a reversal of heat flow, challenging classical thermodynamic expectations. Here, we experimentally demonstrate that internal quantum coherence in a multipartite spin system can also reverse heat flow, without relying on initial correlations with the environment. Under the collision model with cascade interaction, we verify that both the strength and the phase of the coherence term determine the direction and magnitude of energy transfer. These results enable precise control of heat flow using only local quantum properties.
We study the dynamics of heat flux in the thermalization process of a pair of identical quantum systems that interact dissipatively with a reservoir in a cascaded fashion. Despite that the open dynamics of the bipartite system SSS is globally Lindbladian, one of the subsystems ``sees'' the reservoir in a state modified by the interaction with the other subsystem and hence it undergoes a non-Markovian dynamics. As a consequence, the heat flow exhibits a nonexponential time behavior which can greatly deviate from the case where each party is independently coupled to the reservoir. We investigate both thermal and correlated initial states of SSS and show that the presence of correlations at the beginning can considerably affect the heat-flux rate. We carry out our study in two paradigmatic cases---a pair of harmonic oscillators with a reservoir of bosonic modes and two qubits with a reservoir of fermionic modes---and compare the corresponding behaviors. In the case of qubits and for initial thermal states, we find that the trace distance discord is at any time interpretable as the correlated contribution to the total heat flux.
Heat spontaneously flows from hot to cold in standard thermodynamics. However, the latter theory presupposes the absence of initial correlations between interacting systems. We here experimentally demonstrate the reversal of heat flow for two quantum correlated spins-1/2, initially prepared in local thermal states at different effective temperatures, employing a Nuclear Magnetic Resonance setup. We observe a spontaneous energy flow from the cold to the hot system. This process is enabled by a trade off between correlations and entropy that we quantify with information-theoretical quantities. These results highlight the subtle interplay of quantum mechanics, thermodynamics and information theory. They further provide a mechanism to control heat on the microscale.
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.