Open quantum systems coupled to finite baths: A hierarchy of master equations.

An open quantum system in contact with an infinite bath approaches equilibrium, while the state of the bath remains unchanged. If the bath is finite, the open system still relaxes to equilibrium but it induces a dynamical evolution of the bath state. In this paper, we study the dynamics of open quantum systems in contact with finite baths.

Clausius inequality for finite baths reveals universal efficiency improvements.

We study entropy production in nanoscale devices, which are coupled to finite heat baths. This situation is of growing experimental relevance, but most theoretical approaches rely on a formulation of the second law valid only for infinite baths. We fix this problem by pointing out that Clausius' paper from 1865 already contains an adequate formulation of the second law for finite heat baths, which can be also rigorously derived from a microscopic quantum description.

Autonomous Implementation of Thermodynamic Cycles at the Nanoscale.

There are two paradigms to study nanoscale engines in stochastic and quantum thermodynamics. Autonomous models, which do not rely on any external time dependence, and models that make use of time-dependent control fields, often combined with dividing the control protocol into idealized strokes of a thermodynamic cycle. While the latter paradigm offers theoretical simplifications, its utility in practice has been questioned due to the involved approximations.

Reply to "Comment on 'Measurability of nonequilibrium thermodynamics in terms of the Hamiltonian of mean force' ".

We refute the criticism expressed in a Comment by P. Talkner and P. Hänggi [Phys.

Measurability of nonequilibrium thermodynamics in terms of the Hamiltonian of mean force.

The nonequilibrium thermodynamics of an open (classical or quantum) system in strong contact with a single heat bath can be conveniently described in terms of the Hamiltonian of mean force. However, the conventional formulation is limited by the necessity to measure differences in equilibrium properties of the system-bath composite. We make use of the freedom involved in defining thermodynamic quantities, which leaves the thermodynamics unchanged, to show that the Hamiltonian of mean force can be inferred from measurements on the system alone, up to that irrelevant freedom.