Stochastic thermodynamics in the quantum regime

In this paper, we show that correlated coherent states (CCSs) are the most adequate candidates for the role of quantum analogues of the thermal states. The main result of our study reduces to the fact that quantum thermal effects under conditions of the equilibrium of an object with the stochastic environment at any temperatures can be explained consistently only on the basis of the set of CCSs.

We investigate the entropic consequences of the relaxation of an open two-level quantum system towards a thermalised statistical state, using a framework of quantum state diffusion with a minimal set of raising and lowering Lindblad operators. We demonstrate that thermalisation starting from a general state is accompanied by a persistent non-zero mean rate of change of the environmental component of stochastic entropy production. This thermodynamic signature can be associated...

We develop a general theory describing the thermodynamical behavior of open quantum systems coupled to thermal baths beyond perturbation theory. Our approach is based on the exact time-local quantum master equation for the reduced open system states, and on a principle of minimal dissipation. This principle leads to a unique prescription for the decomposition of the master equation into a Hamiltonian part representing coherent time evolution and a dissipator part describing d...

We consider continuously monitored quantum systems and introduce definitions of work and heat along individual quantum trajectories that are valid for coherent superpositions of energy eigenstates. We use these quantities to extend the first and second laws of stochastic thermodynamics to the quantum domain. We illustrate our results with the case of a weakly measured driven two-level system and show how to distinguish between quantum work and heat contributions. We finally e...

According to the Second Law of thermodynamics, the evolution of physical systems has a preferred direction, that is characterized by some positive entropy production. Here we propose a direct way to measure the stochastic entropy produced while driving a quantum open system out of thermal equilibrium. The driving work is provided by a quantum battery, the system and the battery forming an autonomous machine. We show that the battery's energy fluctuations equal work fluctuatio...

In classical thermodynamic processes the unavoidable presence of irreversibility, quantified by the entropy production, carries two energetic footprints: the reduction of extractable work from the optimal, reversible case, and the generation of a surplus of heat that is irreversibly dissipated to the environment. Recently it has been shown that in the quantum regime an additional quantum irreversibility occurs that is linked to decoherence into the energy basis. Here we emplo...

In nano-scale systems coupled to finite-size reservoirs, the reservoir temperature may fluctuate due to heat exchange between the system and the reservoirs. To date, a stochastic thermodynamic analysis of heat, work and entropy production in such systems is however missing. Here we fill this gap by analyzing a single-level quantum dot tunnel coupled to a finite-size electronic reservoir. The system dynamics is described by a Markovian master equation, depending on the fluctua...

Stochastic thermodynamics and the associated fluctuation relations provide the means to extend the fundamental laws of thermodynamics to small scales and systems out of equilibrium. The fluctuating thermodynamic variables are usually treated in the context of either isolated Hamiltonian evolution, or Markovian dynamics in open systems. However, there is no reason a priori why the Markovian approximation should be valid in driven systems under non-equilibrium conditions. In th...

We present the non-Markovian generalization of the widely used stochastic Schrodinger equation. Our result allows to describe open quantum systems in terms of stochastic state vectors rather than density operators, without approximation. Moreover, it unifies two recent independent attempts towards a stochastic description of non-Markovian open systems, based on path integrals on the one hand and coherent states on the other. The latter approach utilizes the analytical propert...

We discuss the role of quantum coherence in the energy fluctuations of open quantum systems. To this aim, we introduce an operational protocol, to which we refer to as the end-point-measurement scheme, allowing to define the statistics of energy changes as a function of energy measurements performed only after its evolution. At the price of an additional uncertainty on the value of the initial energies, this approach prevents the loss of initial quantum coherences and enables...