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.
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.
Quantum coherence is a central resource in quantum information science, yet general frameworks and constraints governing its dynamics remain limited. Although quantum coherence lacks a general monotonicity law, we establish an exact integral fluctuation theorem (FT) for coherence dynamics, formulated in terms of Kirkwood-Dirac (KD) quasiprobability trajectories and valid for arbitrary initial states and dynamics. This integral FT deviates from the standard unit-valued form, and the complex deviation, termed the anomaly, quantifies a weighted overlap between the residual final-state coherence and the coherence generated from the dephased input. The real part of the anomaly yields bounds on coherence change, while its imaginary part constrains the second-order moment of the stochastic coherence change weighted by the imaginary parts of the KD quasiprobabilities. Our results establish general statistical constraints on coherence dynamics, demonstrating the utility and broad applicability of FTs for studying quantum-resource dynamics.
Abstract Just a few years after the inception of quantum mechanics, there has been a research program using the nonclassical values of some quasiprobability distributions to delineate the nonclassical aspects of quantum phenomena. In particular, in Kirkwood–Dirac (KD) quasiprobability distribution, the distinctive quantum mechanical feature of noncommutativity which underlies many nonclassical phenomena, manifests in the nonreal values and/or the negative values of the real part. Here, we develop a faithful quantifier of quantum coherence based on the KD nonclassicality which captures simultaneously the nonreality and the negativity of the KD quasiprobability. The KD-nonclassicality coherence thus defined, is upper bounded by the uncertainty of the outcomes of measurement described by a rank-1 orthogonal projection-valued measure (PVM) corresponding to the incoherent orthonormal basis which is quantified by the Tsallis 1 2 -entropy. Moreover, they are identical for pure states so that the KD-nonclassicality coherence for pure state admits a simple closed expression in terms of measurement probabilities. We then use the Maassen–Uffink uncertainty relation for min-entropy and max-entropy to obtain a lower bound for the KD-nonclassicality coherence of a pure state in terms of optimal guessing probability in measurement described by a PVM noncommuting with the incoherent orthonormal basis. We also derive a trade-off relation for the KD-nonclassicality coherences of a pure state relative to a pair of noncommuting orthonormal bases with a state-independent lower bound. Finally, we sketch a variational scheme for a direct estimation of the KD-nonclassicality coherence based on weak value measurement and thereby discuss its relation with quantum contextuality.
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.
The thermodynamic uncertainty relation (TUR) imposes a fundamental constraint between current fluctuations and entropy production, providing a refined formulation of the second law for micro- and nanoscale systems. Quantum violations of the classical TUR reveal genuinely quantum thermodynamic effects, which are essential for improving performance and enabling optimization in quantum technologies. In this work, we analyze the TUR in a class of paradigmatic quantum thermal-machine models whose operation is enabled by coherent coupling between two energy levels forming a virtual qubit. Steady-state coherences are confined to this virtual-qubit subspace, while in the absence of coherent coupling the system satisfies detailed balance with the thermal reservoirs and supports no steady-state heat currents. We show that the steady-state currents and entropy production can be fully reproduced by an effective classical Markov process, whereas current fluctuations acquire an additional purely quantum correction originating from coherence. As a result, the thermodynamic uncertainty naturally decomposes into a classical (diagonal) contribution and a coherent contribution. The latter becomes negative under resonant conditions and reaches its minimum at the coupling strength that maximizes steady-state coherence. We further identify the conditions for minimizing the thermodynamic uncertainty, and the criteria for surpassing the classical TUR bound in the vicinity of the reversible limit.
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.
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.