Abstract
We establish quantum thermodynamics for open quantum systems weakly coupled to their reservoirs when the system exhibits degeneracies. The first and second law of thermodynamics are derived, as well as a finite-time fluctuation theorem for mechanical work and energy and matter currents. Using a double quantum dot junction model, local eigenbasis coherences are shown to play a crucial role on thermodynamics and on the electron counting statistics.
Highlights
The study of nonequilibrium open quantum systems is an active field of research with particular relevance to routinely-devised systems, such as quantum dots, or electronic circuits [1,2,3,4], or assemblies of cold atoms [5,6,7], for example
We show that coherences cause a bi-modality in the finite time current distribution [38], which is compatible with the fluctuation theorem symmetry
We established the first and and second law, as well as a finite-time fluctuation theorem solely expressed in terms of the mechanical work and the energy and particle counting statistics
Summary
The study of nonequilibrium open quantum systems is an active field of research with particular relevance to routinely-devised systems, such as quantum dots, or electronic circuits [1,2,3,4], or assemblies of cold atoms [5,6,7], for example. For many processes that only depend on populations or for steady state dynamics where eigenstates coherences are always vanishing, a classical stochastic thermodynamics (ST) [19,20,21] can be built for the population dynamics This provides a consistent framework for the study of the thermodynamics of open quantum systems at both the average and the single trajectory level [22,23,24,25,26,27,28]. Open quantum systems with degenerate system energies constitute another important case in which eigenstate coherences come into play already in the weak coupling limit In this case, time-dependent driving is not even required, and coherences may survive even at steady state. We further obtain the counting statistics of the mechanical work and energy and particle currents from the aforementioned quantum master equation and derive a finite time fluctuation theorem that extends its classical counterpart [34] to quantum systems with eigenstate coherences.
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