Frank Redig (TU Delft)

Large deviations for non-equilibrium steady states

Thursday, 18 December 2025, 16:00-17:00 in HG00.062

Abstract

I will start with introducing some background and history on the study of non-equilibrium systems. Then we will focus on a class of systems on a one-dimensional lattice {1,…,N}, coupled to reservoirs at left and right ends. When the reservoir parameters are not equal, the stationary distribution of such as system is called a non-equilibrium steady state. Non-equilibrium refers to the absence of reversibility, visible e.g. via the presence of currents. The expected density profile is linear, and we are interested in understanding the probability of deviating from it in the large system size. This is called a large deviation probability, and typically we have an associated ``rate function’’ , which quantifies the exponentially small probabilities to deviate from the expected linear profile. The large deviation rate function is rarely available in explicit form. We show that for a special family of models, the non-equilibrium steady state can be obtained in a very explicit form, and consequently the large deviation rate function can be computed. A basic technique to handle the models is ``intertwining’’ which allows to pass from the original process to a simpler so-called hidden parameter model. The latter has a Markovian structure in space, and is therefore exactly solvable.

(This talk is based on joint works with C. Giardina, Berend van Tol et al.)