In ergodic physical systems, time-averaged quantities converge (for large times) to their
ensemble-averaged values. Large deviation theory describes rare events where these time …

We consider the problem of conditioning a Markov process on a rare event and of
representing this conditioned process by a conditioning-free process, called the effective or …

We derive a universal bound on generalized currents in Langevin systems in terms of the
mean-square fluctuations of the current and the total entropy production. This bound …

Generalizations of the microcanonical and canonical ensembles for paths of Markov
processes have been proposed recently to describe the statistical properties of …

We present an approach to response around arbitrary out-of-equilibrium states in the form of
a fluctuation–response inequality (FRI). We study the response of an observable to a …

We derive a variational expression for the correlation time of physical observables in steady-
state diffusive systems. As a consequence of this variational expression, we obtain lower …

Active work measures how far the local self-forcing of active particles translates into real
motion. Using population Monte Carlo methods, we investigate large deviations in the active …

We discuss the Giardinà-Kurchan-Peliti population dynamics method for evaluating large
deviations of time-averaged quantities in Markov processes [Phys. Rev. Lett. 96, 120603 …

We introduce a continuous time-reversal operation which connects the time-forward and
time-reversed trajectories in the steady state of an irreversible Markovian dynamics via a …

We study the large deviations of the time-integrated current for a driven diffusion on the
circle, often used as a model of nonequilibrium systems. We obtain the large deviation …