Process interpretation of current entropic bounds

Abstract

We show for Markov diffusion processes that the quadratic entropic bound, recently derived for the rate functions of nonequilibrium currents, can be seen as being produced by an effective process that creates current fluctuations in a sub-optimal way by modifying only the non-reversible part of the drift or force of the process considered while keeping its reversible part constant. This provides a clear interpretation of the bound in terms of a physical process, which explains, among other things, its relation to the fluctuation relation, linear response, and reversible limits. The existence of more general quadratic bounds, and related uncertainty relations, for physical quantities other than currents is also discussed.