Stochastic thermodynamics as reviewed here systematically provides a framework for
extending the notions of classical thermodynamics such as work, heat and entropy …

Stationary nonequilibrium states describe steady flows through macroscopic systems.
Although they represent the simplest generalization of equilibrium states, they exhibit a …

Active-matter systems operate far from equilibrium because of the continuous energy
injection at the scale of constituent particles. At larger scales, described by coarse-grained …

Stochastic heat engines can be built using colloidal particles trapped using optical tweezers.
Here we review recent experimental realizations of microscopic heat engines. We first revisit …

The total entropy production quantifies the extent of irreversibility in thermodynamic systems,
which is nonnegative for any feasible dynamics. When additional information such as the …

Atypical, rare trajectories of dynamical systems are important: they are often the paths for
chemical reactions, the haven of (relative) stability of planetary systems, the rogue waves …

We analyze biased ensembles of trajectories for diffusive systems. In trajectories biased
either by the total activity or the total current, we use fluctuating hydrodynamics to show that …

We derive a general fluctuation theorem for quantum maps. The theorem applies to a broad
class of quantum dynamics, such as unitary evolution, decoherence, thermalization, and …

Every hypothesis must derive indubitable results from mechanically well-defined
assumptions by mathematically correct methods. If the results agree with a large series of …

We study the statistics, in stationary conditions, of the work W τ done by the active force in
different systems of self-propelled particles in a time τ. We show the existence of a critical …