Nonequilibrium Response for Markov Jump Processes: Exact Results and Tight Bounds

The generalization of response theory for open systems far from equilibrium is a central pursuit in nonequilibrium statistical physics. It holds practical importance in biochemical applications, including the characterization of homeostasis, the design of resilient nanotechnologies, the detection of critical transitions, and metabolic control.

We study the static response of Markov jump processes. Using stochastic thermodynamics, we develop a novel approach based on simple linear algebra, which allows us to go beyond currently known results. We first derive a simple and elegant expression for the static response to arbitrary perturbations. Considering the class of Arrhenius-like kinetic parameters we derive novel and simple expressions for the response of edge currents and traffic to kinetic barriers and driving forces perturbations. For the response to energy perturbations, we straightforwardly recover results obtained using nontrivial graph-theoretical methods. We furthermore derive four remarkably simple bounds for the current and traffic, which can be added to the list of simple bounds valid far-from-equilibrium, together with thermodynamic uncertainty relations and speed limits. The bounds show conditions when the responses can be saturated or suppressed. These results are published in [1]. Moving beyond the Arrhenius parameterization, we find the general linear constraints for state and current responses. With these linear relations at hand, we can describe how perturbations of different natures (kinetic parameters and fundamental forces) correlate with each other, providing additional insights for controlling nonequilibrium responses.

[1] Aslyamov Timur, and Massimiliano Esposito. "Nonequilibrium Response for Markov Jump Processes: Exact Results and Tight Bounds." arXiv preprint arXiv:2308.04260 (2023).