Tighter thermodynamic bound on speed limit in systems with unidirectional transitions

TL;DR

This paper derives a tighter thermodynamic speed limit for systems with unidirectional transitions, accounting for resetting entropy production, and refines the bound through optimization, with numerical validation on reset systems.

Contribution

It introduces a new thermodynamic bound considering unidirectional links and resets, providing analytical expressions and an optimization-based refinement.

Findings

Derived a thermodynamic speed limit incorporating unidirectional transitions.

Established uncertainty relations for resetting entropy production moments.

Validated results through numerical simulations of reset systems.

Abstract

We consider a general discrete state-space system with both unidirectional and bidirectional links. In contrast to bidirectional links, there is no reverse transition along the unidirectional links. Herein, we first compute the statistical length and the thermodynamic cost function for transitions in the probability space, highlighting contributions from total, environmental, and resetting (unidirectional) entropy production. Then, we derive the thermodynamic bound on the speed limit to connect two distributions separated by a finite time, showing the effect of the presence of unidirectional transitions. Novel uncertainty relationships can be found for the \textit{temporal} first and second moments of the average resetting entropy production. We derive simple expressions in the limit of slow unidirectional transition rates. Finally, we present a refinement of the thermodynamic bound, by means of an optimization procedure. We numerically investigate these results on systems that stochastically reset with constant and periodic resetting rate.