Thermal noise suppression: how much does it cost?

TL;DR

This paper investigates the minimal energetic cost of suppressing thermal noise in overdamped systems, demonstrating that constant control parameters are optimal and exploring implications for systems with noisy controls.

Contribution

It establishes that constant control parameters minimize noise suppression cost in overdamped systems and analyzes effects of noisy controls through a Brownian particle case study.

Findings

Constant control parameters achieve minimal suppression cost.

Additional modulation increases the cost.

Implications for systems with noisy control parameters are discussed.

Abstract

In order to stabilize the behavior of noisy systems, confining it around a desirable state, an effort is required to suppress the intrinsic noise. This noise suppression task entails a cost. For the important case of thermal noise in an overdamped system, we show that the minimum cost is achieved when the system control parameters are held constant: any additional deterministic or random modulation produces an increase of the cost. We discuss the implications of this phenomenon for those overdamped systems whose control parameters are intrinsically noisy, presenting a case study based on the example of a Brownian particle optically trapped in an oscillating potential.