Year: 2023
Type: preprint
Abstract: We consider a finite-state, continuous-time Markov process, represented in the "linear framework" by a directed graph with labelled edges which specifies the infinitesimal generator of the process. If the graph is strongly connected, the process has a unique steady-state probability distribution, $p$, which may not be one of thermodynamic equilibrium. If the label (rate) of any edge (transition) is perturbed, to reach the new steady-state probability distribution $p'$, we find that the Kullback-Leibler (KL) divergence between these distributions is bounded by the change in the thermodynamic affinity, $ΔA(C)$, of any cycle, $C$, that includes the altered transition, D$_{KL}$$(p'||p) \leq |ΔA(C)|$, irrespective of the structure of the graph. It follows that, if an equilibrium distribution is shifted away from equilibrium by perturbing a single rate, then the free energy difference between these distributions is similarly bounded $F^{neq}-F^{eq}\leq |ΔA(C)|$. Our analysis reveals universal, energy-induced bounds on the information-processing capabilities of Markov systems operating arbitrarily far from thermodynamic equilibrium.
Source: arXiv (Cornell University)
Authors: Cetiner, Ugur, Gunawardena, Jeremy
Institution: Harvard University
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4387725556