arXiv subjects

Ugur Cetiner

Publications and source records attributed to Ugur Cetiner.

3 recordsLinked to original sources

arXiv2024

A Jarzynski-type equality for nonequilibrium steady-state probabilities

We show that steady-state probabilities of a nonequilibrium Markovian system can be reconstructed from a weighted ensemble average of finite-time loop-erased paths. Each path $Γ$ is weighted by $e^{-S(Γ)}$, where $S(Γ)$ can be interpreted either as the action functional or as the entropy change in the surrounding reservoirs. In doing so, we uncover a Jarzynski-type equality for nonequilibrium steady states. We also reveal that the probabilities of loop-erased paths obey strong thermodynamic symmetry relations.

cond-mat.stat-mech↗

arXiv2023

Universal Bounds on Information-Processing Capabilities of Markov Processes

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.

physics.bio-ph↗

arXiv2021

Reformulating non-equilibrium steady-states and generalised Hopfield discrimination

Despite substantial progress in non-equilibrium physics, steady-state (s.s.) probabilities remain intractable to analysis. For a Markov process, s.s. probabilities can be expressed in terms of transition rates using the Matrix-Tree theorem (MTT) in the graph-based linear framework. The MTT reveals that, away from equilibrium, s.s. probabilities become globally dependent on all rates, with expressions growing exponentially in the system size. This overwhelming complexity and lack of thermodynamic interpretation have greatly impeded analysis. Here, we show that s.s. probabilities are proportional to the average of $\exp(-S(P))$, where $S(P)$ is the entropy generated along minimal paths, $P$, in the graph, and the average is taken over a probability distribution on spanning trees. Assuming Arrhenius rates, this "arboreal" distribution becomes Boltzmann-like, with the energy of a tree being its total edge barrier energy. This reformulation offers a thermodynamic interpretation that smoothly generalises equilibrium statistical mechanics and reorganises the expression complexity: the number of distinct minimal-path entropies depends on the entropy production index, a new graph-theoretic measure of non-equilibrium complexity, not on graph size. We demonstrate the power of this reformulation by extending Hopfield's analysis of discrimination by kinetic proofreading to any graph with index 1. We derive a general formula for the error ratio and use it to show that local energy dissipation can yield optimal discrimination through global synergy.

cond-mat.stat-mech↗