Optimality of non-conservative driving for finite-time processes with discrete states

TL;DR

This paper proves that for finite-time processes with discrete states, optimal driving involves non-conservative forces, contrasting with continuous systems, and establishes bounds related to network structure and asymmetry.

Contribution

It demonstrates that optimal finite-time control in discrete systems requires non-conservative driving and derives bounds based on network cycles and asymmetry.

Findings

Optimal process involves non-conservative driving in discrete systems.

Bound on driving affinity depends on cycle size in multicyclic networks.

Asymmetry in rates influences the bounds on optimal driving affinity.

Abstract

An optimal finite-time process drives a given initial distribution to a given final one in a given time at the lowest cost as quantified by total entropy production. We prove that for system with discrete states this optimal process involves non-conservative driving, i.e., a genuine driving affinity, in contrast to the case of system with continuous states. In a multicyclic network, the optimal driving affinity is bounded by the number of states within each cycle. If the driving affects forward and backwards rates non-symmetrically, the bound additionally depends on a structural parameter characterizing this asymmetry.