Abstract
We study the coarse-graining approach to derive a generator for the evolution of an open quantum system over a finite time interval. The approach does not require a secular approximation but nevertheless generally leads to a Lindblad–Gorini–Kossakowski–Sudarshan generator. By combining the formalism with full counting statistics, we can demonstrate a consistent thermodynamic framework, once the switching work required for the coupling and decoupling with the reservoir is included. Particularly, we can write the second law in standard form, with the only difference that heat currents must be defined with respect to the reservoir. We exemplify our findings with simple but pedagogical examples.
Highlights
With the advent of an era where the promises of quantum computation [1] are approached in laboratories, one has to face the problem that controlled quantum systems are inevitably coupled to the outside world
This has sparked ideas to explore the potential of open quantum systems as quantum heat engines [14], which is nowadays part of a somewhat larger research field called quantum thermodynamics [15]
We have constrained ourselves to fixed coarse-graining times, for which we can write the second law in differential form, since the usual LGKS formalism, albeit with differently defined energy currents, applies
Summary
With the advent of an era where the promises of quantum computation [1] are approached in laboratories, one has to face the problem that controlled quantum systems are inevitably coupled to the outside world. For a reservoir in thermal equilibrium, the dynamical map obtained this way will drag the system density matrix towards the local thermal equilibrium state of the system (which does not depend on the system-reservoir coupling characteristics) and has a transparent thermodynamic interpretation [11,12,13]. This has sparked ideas to explore the potential of open quantum systems as quantum heat engines [14], which is nowadays part of a somewhat larger research field called quantum thermodynamics [15].
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