Logarithmic susceptibility and optimal control of large fluctuations

TL;DR

This paper investigates how external fields influence rare large fluctuations in systems, introducing a logarithmic susceptibility concept to optimize control strategies, revealing singular behaviors in activation energies under nonadiabatic conditions.

Contribution

It introduces the concept of logarithmic susceptibility for analyzing and controlling large fluctuations in driven systems, including nonadiabatic effects on activation energies.

Findings

Logarithm of fluctuation probability is linear in field magnitude across a broad range.

Logarithmic susceptibility effectively characterizes system response to external fields.

Activation energies exhibit singular behavior with respect to field shape in nonadiabatic regimes.

Abstract

We analyze the probabilities of large infrequent fluctuations in systems driven by external fields. In a broad range of the field magnitudes, the logarithm of the fluctuation probability is linear in the field magnitude, and the response can be characterized by a logarithmic susceptibility. This susceptibility is used to analyze optimal control of large fluctuations. For nonadiabatic driving, the activation energies for nucleation and for escape of a Brownian particle display singular behavior as a function of the field shape.