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arXiv · 2310.10584

Universal Bounds on Information-Processing Capabilities of Markov Processes

Ugur Cetiner·Jeremy Gunawardena
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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.

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Ugur Cetiner, Jeremy Gunawardena. 2023-10-16. Universal Bounds on Information-Processing Capabilities of Markov Processes. https://arxiv.org/abs/2310.10584

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