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arXiv:2506.05995 · Physical Review A

Anomalous flow in correlated quantum systems: No-go result and multiple-charge scenario

Rui Guan, Junjie Liu

Published Aug 6, 2025• 2 citations
arXivHTMLPDF

Abstract

Correlated quantum systems can exhibit thermodynamic behaviors that defy classical expectations, with anomalous energy flow (AEF) against temperature gradients serving as a paradigmatic example. While AEF has been shown to arise from the consumption of initial quantum correlations, little is known about whether AEF can occur without correlation depletion, or if analogous anomalous transport exists for conserved quantities---dubbed charges---other than energy. Here, we develop a general global-local thermodynamic approach to describe charge exchange between arbitrary correlated quantum systems. For energy-conserving systems, we analytically rule out AEF in initially uncorrelated states, even with the involvement of quantum catalysts, thereby complementing existing studies. In contrast, in systems with multiple conserved charges, we uncover a mechanism for AEF that requires no initial correlations but is instead induced by a drag effect from normal flows of nonenergy charges. Furthermore, by treating all conserved charges on equal footing, we generalize AEF to a broader concept of anomalous charge flow, applicable to any conserved charge. We confirm theoretical expectations with numerical examples. These findings deepen our understanding of nonequilibrium quantum thermodynamics and open new avenues for controlling transport phenomena in correlated quantum systems.

DOI
10.1103/gy6n-5x26

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Correlated quantum systems can exhibit thermodynamic behaviors that defy classical expectations, with anomalous energy flow (AEF) against temperature gradients serving as a paradigmatic example. While AEF has been shown to arise from the consumption of initial quantum correlations, little is known about whether AEF can occur without correlation depletion, or if analogous anomalous transport exists for conserved quantities---dubbed charges---other than energy. Here, we develop a general global-local thermodynamic approach to describe charge exchange between arbitrary correlated quantum systems. For energy-conserving systems, we analytically rule out AEF in initially uncorrelated states, even with the involvement of quantum catalysts, thereby complementing existing studies. In contrast, in systems with multiple conserved charges, we uncover a mechanism for AEF that requires no initial correlations but is instead induced by a drag effect from normal flows of nonenergy charges. Furthermore, by treating all conserved charges on equal footing, we generalize AEF to a broader concept of anomalous charge flow, applicable to any conserved charge. We confirm theoretical expectations with numerical examples. These findings deepen our understanding of nonequilibrium quantum thermodynamics and open new avenues for controlling transport phenomena in correlated quantum systems.
In classical thermodynamics energy always flows from the hotter system to the colder one. However, if these systems are initially correlated, the energy flow can reverse, making the cold system colder and the hot system hotter. This intriguing phenomenon is called "anomalous energy flow" and shows the importance of initial correlations in determining physical properties of thermodynamic systems. Here we investigate the fundamental limits of this effect. Specifically, we find the optimal amount of energy that can be transferred between quantum systems under closed and reversible dynamics, which then allows us to characterize the anomalous energy flow. We then explore a more general scenario where the energy flow is mediated by an ancillary quantum system that acts as a catalyst. We show that this approach allows for exploiting previously inaccessible types of correlations, ultimately resulting in an energy transfer that surpasses our fundamental bound. To demonstrate these findings, we use a well-studied quantum optics setup involving two atoms coupled to an optical cavity.
The application of thermodynamics to quantum systems have been arising great hopes and expectations in regard to thermodynamic tasks - work or energy extraction, and refrigeration. For such tasks, enhancements based on genuine quantum features like coherence and quantum correlations have been recently reported. However, little is known about the relation between such quantum features and a central part the aforementioned thermodynamic tasks, namely energy flows. Here, we introduce a concept of apparent temperature as an extension of the familiar and intuitive concept of temperature to out-of-equilibrium systems. We use it to study the influence of internal coherence and correlations on energy flows between two systems. Measured by the variation of the apparent temperature, we show that internal coherence and correlations affect drastically energy flows, and we give illustrative examples. To complete the picture we recover seminal results providing an interesting alternative point of view of diverse phenomena. Since energy exchanges are omnipresent in thermodynamics, it is expected that our formalism can be exploited in more problems and be decisive in designing future quantum thermal machines.
We study the effect of correlation on the direction of particle exchange between local thermal sub-systems where the total system is isolated. Our focus is the situation where both sub-systems have the same temperature but different chemical potentials to eliminate the effect of energy transfer due to the temperature difference. The analysis is done in two limits; in the short time scale where the final state of each sub-system is close to its initial thermal state and in a longer time scale where each sub-system's final state can be arbitrary. The results indicate that the conventional flow of particles from a higher chemical potential to a lower one occurs when the correlation which is quantified by mutual information increases. In contrast, an anomalous flow of particles in the reverse direction has a chance to happen when the correlation goes down. Our findings show that the direction of the particle exchange cannot be predetermined by the chemical potential difference in the presence of correlation.
Recent research on the thermodynamic arrow of time, at the microscopic scale, has questioned the universality of its direction. Theoretical studies showed that quantum correlations can be used to revert the natural heat flow (from the hot body to the cold one), posing an apparent challenge to the second law of thermodynamics. Such an "anomalous" heat current was observed in a recent experiment (K. Micadei et al., arXiv:1711.03323), by employing two spin systems initially quantum correlated. Nevertheless, the precise relationship between this intriguing phenomenon and the initial conditions that allow it is not fully evident. Here, we address energy transfer in a wider perspective, identifying a nonclassical contribution that applies to the reversion of the heat flow as well as to more general forms of energy exchange. We derive three theorems that describe the energy transfer between two microscopic systems, for arbitrary initial bipartite states. Using these theorems, we obtain an analytical bound showing that certain type of quantum coherence can optimize such a process, outperforming incoherent states. This genuine quantum advantage is corroborated through a characterization of the energy transfer between two qubits. For this system, it is shown that a large enough amount of coherence is necessary and sufficient to revert the thermodynamic arrow of time. As a second crucial consequence of the presented theorems, we introduce a class of nonequilibrium states that only allow unidirectional energy flow. In this way, we broaden the set where the standard Clausius statement of the second law applies.
We extend the exchange fluctuation theorem for energy exchange between thermal quantum systems beyond the assumption of molecular chaos, and describe the nonequilibrium exchange dynamics of correlated quantum states. The relation quantifies how the tendency for systems to equilibrate is modified in high-correlation environments. In addition, a more abstract approach leads us to a "correlation fluctuation theorem". Our results elucidate the role of measurement disturbance for such scenarios. We show a simple application by finding a semiclassical maximum work theorem in the presence of correlations. We also present a toy example of qubit-qudit heat exchange, and find that non-classical behaviour such as deterministic energy transfer and anomalous heat flow are reflected in our exchange fluctuation theorem.
Anomalous heat transfer (AHT), a process by which heat spontaneously flows from a cold system into a hot one, superficially contradicts the Clausius statement of the second law of thermodynamics. Here we provide a full classification of mechanisms of AHT in nonequilibrium quantum systems from a quantum-information perspective. For initial states in local equilibrium, we find that AHT can arise from three resources: initial correlation, intrasystem interaction, and intrasystem temperature inhomogeneity. In particular, for qubit systems, we prove that initial quantum coherence is necessary for AHT if the intersystem interactions are limited to the two-body type. We explicitly show AHT dominated by each of the mechanisms in a three-qubit system. Our classification scheme may offer a guideline for developing high-efficiency quantum autonomous thermal machines.