Near-optimality of conservative driving in discrete systems

TL;DR

This paper investigates the efficiency of conservative versus nonconservative driving protocols in discrete systems, showing that conservative protocols can be at most twice as dissipative as the optimal nonconservative ones, with implications for control in complex networks.

Contribution

It demonstrates that in discrete systems, conservative protocols are near-optimal, with dissipation at most twice the minimum, and provides explicit examples illustrating this bound.

Findings

Conservative protocols are at most twice as dissipative as optimal nonconservative ones.

Nonconservative forces are necessary for optimal transport in complex topologies.

Explicit example shows the order of improvement achievable by nonconservative driving.

Abstract

Transferring a physical system from an initial to a final state while minimizing energetic losses is an interdisciplinary control problem that bridges stochastic thermodynamics and optimal transport theory. Recent research typically considers problems in which the optimal solution is realized via conservative forces, but whether this situation applies depends on the problem's constraints. In systems with complex topologies like discrete networks, the optimal, dissipation-minimizing protocol involves applying nonconservative forces along cycles if the timescales of the transitions in the network are fixed. We show that although nonconservative driving is optimal in this setting, a conservative protocol exists whose dissipation is at most twice the optimal one. This finding is complemented with an example modeling transport across an energy barrier, which illustrates such improvements of order 1 explicitly. Qualitatively, conservative driving falls short of achieving optimality because direct transport across the barrier is avoided. We conclude with a discussion that the optimality of nonconservative driving might be a generic phenomenon: As fewer degrees of freedom can be optimized, additional degrees of freedom due to adding nonconservative forces become more significant.