Abstract Fluctuation theorems (FT) reveal crucial properties about the nature of non-equilibrium dynamics by constraining the statistical distribution of quantities such as heat, work and entropy production. Here, we report theoretical and experimental results regarding two FT for a new quantity, named coherent energy, which is an energy form directly associated with the coherences of a quantum state. The FT are verified using the two-point measurement protocol with an all-optical setup in which the system information is encoded in the polarization of one photon of a pair. From the outcomes of our experiment we directly assess the energy probability distributions. We also demonstrate an universal bound on the energy of thermal states under the action of unitary operations, which could be the first step to establish an arrow of time for reversible processes.
Abstract Fluctuation theorems (FT) reveal crucial properties about the nature of non-equilibrium dynamics by constraining the statistical distribution of quantities such as heat, work and entropy production. Here, we report theoretical and experimental results regarding two FT for a new quantity, named coherent energy, which is an energy form directly associated with the coherences of a quantum state. The FT are verified using the two-point measurement protocol with an all-optical setup in which the system information is encoded in the polarization of one photon of a pair. From the outcomes of our experiment we directly assess the energy probability distributions. We also demonstrate an universal bound on the energy of thermal states under the action of unitary operations, which could be the first step to establish an arrow of time for reversible processes.
The principle of microscopic reversibility lies at the core of fluctuation theorems, which have extended our understanding of the second law of thermodynamics to the statistical level. In the quantum regime, however, this elementary principle should be amended as the system energy cannot be sharply determined at a given quantum phase space point. In this Letter, we propose and experimentally test a quantum generalization of the microscopic reversibility when a quantum system interacts with a heat bath through energy-preserving unitary dynamics. Quantum effects can be identified by noting that the backward process is less likely to happen in the existence of quantum coherence between the system's energy eigenstates. The experimental demonstration has been realized by mixing coherent and thermal states in a beam splitter, followed by heterodyne detection in an optical setup. We verify that the quantum modification for the principle of microscopic reversibility is critical in the low-temperature limit, while the quantum-to-classical transition is observed as the temperature of the thermal field gets higher.
Fluctuation theorems are one of the pillars of nonequilibrium thermodynamics. Broadly speaking, they concern the statistical distribution of quantities such as heat, work, or entropy production. Quantum experiments, however, usually can only assess these distributions indirectly, or reconstruct them a posteriori. In this Letter we report an experiment where the distribution of entropy production is obtained directly from the outcomes (clicks) of an optical experiment simulating the interaction between a two-level system and a thermal reservoir. The setup consists of entangled photon pairs, one of which is sent to an interferometer implementing a finite-temperature amplitude damping channel, and is designed so as to allow full access to the two-point measurement statistics of both system and reservoir. First, by measuring the entangled pair, we directly implement the two-point measurement scheme in the system, avoiding the destructive nature of photodetection. Second, each optical path of the interferometer is associated with a specific transition of the reservoir. Thus, by blocking all but one of the paths, we can measure the conditional entropy production, given a specific reservoir trajectory.
Abstract Thermodynamic irreversibility is well characterized by the entropy production arising from non-equilibrium quantum processes. We show that the entropy production of a quantum system undergoing open-system dynamics can be formally split into a term that only depends on population unbalances, and one that is underpinned by quantum coherences. This allows us to identify a genuine quantum contribution to the entropy production in non-equilibrium quantum processes. We discuss how these features emerge both in Lindblad-Davies differential maps and finite maps subject to the constraints of thermal operations. We also show how this separation naturally leads to two independent entropic conservation laws for the global system-environment dynamics, one referring to the redistribution of populations between system and environment and the other describing how the coherence initially present in the system is distributed into local coherences in the environment and non-local coherences in the system-environment state. Finally, we discuss how the processing of quantum coherences and the incompatibility of non-commuting measurements leads to fundamental limitations in the description of quantum trajectories and fluctuation theorems.
We prove the second law of thermodynamics and the nonequilibrium fluctuation theorem for pure quantum states. The entire system obeys reversible unitary dynamics, where the initial state of the heat bath is not the canonical distribution but is a single energy eigenstate that satisfies the eigenstate-thermalization hypothesis. Our result is mathematically rigorous and based on the Lieb-Robinson bound, which gives the upper bound of the velocity of information propagation in many-body quantum systems. The entanglement entropy of a subsystem is shown connected to thermodynamic heat, highlighting the foundation of the information-thermodynamics link. We confirmed our theory by numerical simulation of hard-core bosons, and observed dynamical crossover from thermal fluctuations to bare quantum fluctuations. Our result reveals a universal scenario that the second law emerges from quantum mechanics, and can be experimentally tested by artificial isolated quantum systems such as ultracold atoms.
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.
Fluctuation theorems are relations constraining the out-of-equilibrium fluctuations of thermodynamic quantities like the entropy production that were initially introduced for classical or quantum systems in contact with a thermal bath. Here we show, in the absence of thermal bath, the dynamics of continuously measured quantum systems can also be described by a fluctuation theorem, expressed in terms of a recently introduced arrow of time measure. This theorem captures the emergence of irreversible behavior from microscopic reversibility in continuous quantum measurements. From this relation, we demonstrate that measurement-induced wave-function collapse exhibits absolute irreversibility, such that Jarzynski-like equalities are violated, and that this property is inherent to quantum information acquisition. We apply our results to different continuous measurement schemes on a qubit: dispersive measurement, homodyne, and heterodyne detection of qubit's fluorescence.