Precision-dissipation trade-off for driven stochastic systems

TL;DR

This paper derives a formula linking the precision of trajectory following in small systems to dissipation limits, providing optimal protocols with applications in information erasure and electronics.

Contribution

It introduces a closed-form expression for the precision-dissipation trade-off and identifies optimal driving protocols conserving distribution shape.

Findings

Dissipation inversely proportional to deviation from target trajectory

Optimal protocols maintain probability distribution shape

Applications in bit erasure and electronic circuits

Abstract

In this paper, I derive a closed expression for how precisely a small-scaled system can follow a pre-defined trajectory, while keeping its dissipation below a fixed limit. The total amount of dissipation is approximately inversely proportional to the expected deviation from the pre-defined trajectory. The optimal driving protocol is derived and it is shown that associated time-dependent probability distribution conserves its shape throughout the protocol. Potential applications are discussed in the context of bit erasure and electronic circuits.