Stochastic paths controlling speed and dissipation

Abstract

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 show that this intuition does not necessarily hold for stochastic processes when there are strong nonequilibrium currents. To analyze the relationship between dissipation and speed, 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 demonstrate that kinetics can sculpt the nonequilibrium path space so that faster structureforming paths dissipate less. The path-level dissipation is largely controlled through the nonequilibrium currents of a dissipative cycle situated between the initial and final states whose relative energies independently control the time to assemble. Overall, these results suggest that minimally dissipative materials, which respond quickly to their environment, may be designed through the stochastic thermodynamics of their path space.