Infinite variety of thermodynamic speed limits with general activities

TL;DR

This paper introduces a unified framework for thermodynamic speed limits (TSLs) based on various activities, deriving an infinite variety of bounds for Markov processes and chemical networks.

Contribution

It unifies existing TSLs using generalized means and derives new bounds for different activities in stochastic and deterministic systems.

Findings

Derived an infinite variety of TSLs using different activities.

Analyzed the tightness of entropy production bounds in various TSLs.

Unified framework encompasses existing and new thermodynamic speed limits.

Abstract

Activity, which represents the kinetic property of dynamics, plays a central role in obtaining thermodynamic speed limits (TSLs). In this paper, we discuss a unified framework that provides the existing TSLs based on different activities such as dynamical activity and dynamical state mobility. This unification is based on generalized means that include standard means such as the arithmetic, logarithmic, and geometric means, the first two of which respectively correspond to the dynamical activity and the dynamical state mobility. We also derive an infinite variety of TSLs for Markov jump processes and deterministic chemical reaction networks using different activities. The lower bound on the entropy production given by each TSL provides the minimum dissipation achievable by a conservative force. We numerically and analytically discuss the tightness of the lower bounds on the EPR in the various TSLs.