Stochastic paths controlling speed and dissipation

TL;DR

This paper investigates the relationship between speed and dissipation in stochastic processes far from equilibrium, deriving exact path probabilities and showing that faster paths can sometimes dissipate less energy under certain conditions.

Contribution

It derives an exact expression for path probabilities of Markov chains and demonstrates how to design kinetic pathways to minimize dissipation while increasing speed.

Findings

Faster processes can dissipate less energy when nonequilibrium currents are strong.

The model links initial/target state energies to process speed and cycle currents to dissipation.

Path-level dissipation can be minimized by controlling nonequilibrium currents.

Abstract

Near equilibrium, thermodynamic intuition suggests that fast, irreversible processes will dissipate more energy and entropy than slow, quasistatic processes connecting the same initial and final states. Here, we test the hypothesis that this relationship between speed and dissipation holds for stochastic processes far from equilibrium. To analyze these processes on finite timescales, we derive an exact expression for the path probabilities of continuous-time Markov chains from the path summation solution of the master equation. Applying this formula to a model for nonequilibrium self-assembly, we show that more speed can lead to less dissipation when there are strong nonequilibrium currents. In the model, the relative energies of the initial and target states control the speed, and the nonequilibrium currents of a cycle situated between these states control the path-level dissipation. This model serves as a minimal prototype for designing kinetics to sculpt the nonequilibrium path space, so that faster structure-forming paths dissipate less.