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arXiv:1909.11116 · PRX Quantum

Quasiprobability Distribution for Heat Fluctuations in the Quantum Regime

Amikam Levy, Matteo Lostaglio

Published Sep 25, 2020• 93 citations
arXivHTMLPDF

Abstract

The standard approach to deriving fluctuation theorems fails to capture the effect of quantum correlation and coherence in the initial state of the system.Here, we overcome this difficulty and derive the heat-exchange-fluctuation theorem in the full quantum regime by showing that the energy exchange between two locally thermal states in the presence of initial quantum correlations is faithfully captured by a quasiprobability distribution.Its negativities, being associated with proofs of contextuality, are proxies of nonclassicality.We discuss the thermodynamic interpretation of negative probabilities and provide heat-flow inequalities that can only be violated in their presence.Remarkably, testing these fully quantum inequalities, at an arbitrary dimension, is no more difficult than testing traditional fluctuation theorems.We test these results on data collected in a recent experiment studying the heat transfer between two qubits and give examples for the capability of witnessing negative probabilities at higher dimensions.

DOI
10.1103/prxquantum.1.010309

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The standard approach to deriving fluctuation theorems fails to capture the effect of quantum correlation and coherence in the initial state of the system.Here, we overcome this difficulty and derive the heat-exchange-fluctuation theorem in the full quantum regime by showing that the energy exchange between two locally thermal states in the presence of initial quantum correlations is faithfully captured by a quasiprobability distribution.Its negativities, being associated with proofs of contextuality, are proxies of nonclassicality.We discuss the thermodynamic interpretation of negative probabilities and provide heat-flow inequalities that can only be violated in their presence.Remarkably, testing these fully quantum inequalities, at an arbitrary dimension, is no more difficult than testing traditional fluctuation theorems.We test these results on data collected in a recent experiment studying the heat transfer between two qubits and give examples for the capability of witnessing negative probabilities at higher dimensions.
We derive a quantum extension of the thermodynamic uncertainty relation where dynamical fluctuations are quantified by the Terletsky-Margenau-Hill quasiprobability, a quantum generalization of the classical joint probability. The obtained inequality plays a complementary role to existing quantum thermodynamic uncertainty relations, focusing on observables' change rather than exchange of charges through jumps and respecting initial coherence. Quasiprobabilities show anomalous behaviors that are forbidden in classical systems, such as negativity; we reveal that negativity or a nonclassically enhanced escape rate is necessary to increase an output-to-dissipation ratio beyond classical limitations and show that the requirements are basis independent and stronger than quantum coherence. To illustrate these statements, we employ a model that can exhibit a dissipationless heat current, which would be prohibited in classical systems; we construct a state that has much coherence but does not lead to a dissipationless current due to the absence of anomalous behaviors in quasiprobabilities.
Quantum fluctuation theorems provide fundamental constraints on entropy production but rely on a trajectory-based description that becomes problematic in the presence of coherence and incompatible measurements. While deviations from standard fluctuation relations in quantum regimes are often attributed to coherence, the precise nonclassical mechanism underlying such effects remains under active discussion. In this work, we investigate contextual interference effects in nonequilibrium thermodynamics using a minimal analytically solvable two-qubit heat-exchange model with a phase-tunable partial-swap interaction. By employing a coherence-preserving Kirkwood–Dirac (KD) quasiprobability formulation of energy exchange, we identify a single correction term, [Formula: see text], that quantifies deviations from the conventional fluctuation-theorem symmetry. We show that this correction originates from interference between incompatible measurement contexts within the degenerate single-excitation subspace and vanishes both in the incoherent limit and at thermal equilibrium. The resulting expression is fully analytic, depends on experimentally tunable parameters, and explicitly connects entropy-current fluctuations to phase-sensitive coherence effects. Our results provide an operationally accessible signature of KD-interference contributions in quantum thermodynamics and demonstrate that coherence, when combined with measurement incompatibility, induces a well-defined correction to fluctuation relations. This establishes a minimal framework linking contextual interference and thermodynamic irreversibility and suggests experimentally feasible routes for probing such effects on current quantum platforms.
The work is a concept of fundamental importance in thermodynamics. An open question is how to describe the work fluctuation for quantum coherent processes in the presence of initial quantum coherence in the energy basis. With the aim of giving a unified description, here we introduce and study a class of quasiprobability distributions of work, which give an average work equal to the average energy change of the system and reduce to the two-projective measurement scheme for an initial incoherent state. Moreover, we characterize the work with the help of fluctuation relations. In particular, by considering the joint distribution of work and initial quantum coherence, we find a fluctuation theorem involving quantum coherence, from which follows a second law of thermodynamics in the case of initial thermal populations. Furthermore, we propose a way to measure the characteristic function of work and we discuss the negativity of the quasiprobability. The effects of coherence are also investigated for a simple system of a qubit.
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.
We investigate a simple model exhibiting a prethermal phase, i.e., a metastable state that emerges before full thermalization, through the framework of quantum stochastic thermodynamics. We explore the effects of quantum coherence in the energy eigenbasis of the initial state of the system on the process of heat exchange with a bath, and their contribution to entropy production as quantified by a heat-exchange fluctuation theorem. Such a relation is derived using the end-point measurement scheme, a protocol that accounts for initial quantum coherence in the statistics of energy exchanges resulting from a nonequilibrium process. We compare these results with those obtained from the widely used two-point measurement scheme, which, by construction, fails to capture such quantum effects.
In classical thermodynamics, heat must spontaneously flow from hot to cold systems. In quantum thermodynamics, the same law applies when considering multipartite product thermal states evolving unitarily. If initial correlations are present, anomalous heat flow can happen, temporarily making cold thermal states colder and hot thermal states hotter. Such an effect can happen due to entanglement but also because of classical randomness, hence lacking a direct connection with nonclassicality. In this work, we introduce scenarios in which anomalous heat flow have a direct link to nonclassicality, defined as the failure of noncontextual models to explain experimental data. We start by extending known noncontextuality inequalities to a setup in which sequential transformations are considered. We then show a class of quantum prepare-transform-measure protocols, characterized by a time interval ( 0 , τ c ) for a given critical time τ c , where anomalous heat flow happens only if a noncontextuality inequality is violated. We also analyze a recent experiment from and find the critical time τ c based on the authors’ experimental parameters. We conclude by investigating heat flow in the evolution of two-qudit systems, showing that our findings are not an artifact of using two-qubit systems.