Entropy production in systems with unidirectional transitions

Abstract

The entropy production is one of the most essential features for systems operating out of equilibrium. The formulation for discrete-state systems goes back to the celebrated Schnakenberg's work and hitherto can be carried out when for each transition between two states also the reverse one is allowed. Nevertheless, several physical systems may exhibit a mixture of both unidirectional and bidirectional transitions, and how to properly define the entropy production in this case is still an open question. Here, we present a solution to such a challenging problem. The average entropy production can be consistently defined, employing a mapping that preserves the average fluxes, and its physical interpretation is provided. We describe a class of stochastic systems composed of unidirectional links forming cycles and detailed-balanced bidirectional links, showing that they behave in a pseudo-deterministic fashion. This approach is applied to a system with time-dependent stochastic resetting. Our framework is consistent with thermodynamics and leads to some intriguing observations on the relation between the arrow of time and the average entropy production for resetting events.

Stochastic resetting and applications

“…In [148] resetting of colloidal particle in a potential was considered and used to obtain a first law of thermodynamics and to identify the thermodynamic work done by resetting. The resetting entropy production rate was derived for this system with space dependent resetting rate r(x) to resetting position X ṙ S reset = dx r(x)p(x) ln p(x) p Xr (8.1) and from this a second law of thermodynamics including resetting was proposed (see also [152]). Building on the identification of entropy change due to resetting, Pal and Rahav [153] considered how integral fluctuation theorems apply to resetting problems.…”

ABC Transporters are billion-year-old Maxwell Demons

“…As expected, independently of the specific cycle considered, as long as it runs according to this rule, it dissipates (see Supp. Info., Section E) 22 which is precisely the net heat released into the environment by opening the door after measure and closing it after the molecule has passed rather than going through the opposite process .…”

Dissipation-driven selection under finite diffusion: hints from equilibrium and separation of time-scales

“…Naively speaking, C equilibrates between both boxes, and the transformation between A and B can be ignored for the steady state, resulting in a positive stationary R CB . Increasing d, in this case, also the reaction between A and C in the cold box becomes slower than diffusion, and the system falls back into the infinite diffusion limit [11,18,23]. When the energy landscape is not flat, i.e.…”

“…Here, we explore more realistic cases in which the diffusion coefficient between two thermal reservoirs at different temperatures is finite and the diffusive time-scale is comparable to the one of chemical transition rates [18]. Interestingly, as a function of the diffusion coefficient, the system may experience sharp transitions between phases with different selection strengths.…”