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.
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.
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.
Quantum coherence has been shown to impact the operational capabilities of quantum systems performing thermodynamic tasks in a significant way, and yet the possibility and conditions for genuine coherence-enhanced thermodynamic operation remain unclear. Introducing a comparison with classical machines using the same set of thermodynamic resources, we show that for steady-state quantum thermal machines – both autonomous and externally driven – that interact weakly with thermal reservoirs and work sources, the presence of coherence induced by perturbations in the machine Hamiltonian guarantees a genuine thermodynamic advantage under mild conditions. This advantage applies to both cases where the induced coherence is between levels with different energies or between degenerate levels. On the other hand, we show that engines subjected to noise-induced coherence can be outperformed by classical stochastic engines using exactly the same set of (incoherent) resources. We illustrate our results with three prototypical models of heat engines and refrigerators: the three-level amplifier, the three-qubit autonomous refrigerator, and a noise-induced-coherence machine.
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.
Temperature is one of the central concepts of thermodynamics, yet its meaning far from equilibrium remains unclear. The problem is especially challenging in isolated quantum many-body systems, whose states evolve unitarily, may remain far from equilibrium, and retain energy coherence, a genuinely quantum feature with no direct classical counterpart. Specifically, energy fluctuations in a nonstationary quantum state have two distinct origins. Part of these fluctuations comes from uncertainty in the energy populations and has the usual thermodynamic meaning. The rest comes from quantum coherence between energy sectors and is responsible for the state's time dependence. We propose that, even away from equilibrium, temperature identifies the state within the family of regular states sharing the same energy-coherence structure. The resulting inverse temperature is obtained from a principle of minimum discrimination information, which selects the least distinguishable state compatible with the prescribed energy and coherence structure. This replaces the usual maximum-entropy principle, which, applied naively, can yield a biased estimator of the inverse temperature. We also lay the groundwork for an extension of the construction to subsystems and show that, although the inverse temperature of a subsystem is not determined by its reduced state alone, under an alignment assumption, its instantaneous rate of change is a local quantity for sufficiently large subsystems.
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.
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.