Convergence to the asymptotic large deviation limit

TL;DR

This study experimentally investigates how finite data affects the convergence of large deviation estimators for work and heat in a levitated nanoparticle under feedback control, revealing the critical influence of singular prefactors.

Contribution

It introduces a criterion to determine the convergence domain of large deviation estimators without prior knowledge of probability distributions.

Findings

Singular prefactors significantly restrict convergence.

The criterion effectively identifies convergence domains.

Experimental results highlight the role of subexponential factors.

Abstract

Large deviation theory offers a powerful and general statistical framework to study the asymptotic dynamical properties of rare events. The application of the formalism to concrete experimental situations is, however, often restricted by finite statistics. Data might not suffice to reach the asymptotic regime or judge whether large deviation estimators converge at all. We here experimentally investigate the large deviation properties of the stochastic work and heat of a levitated nanoparticle subjected to nonequilibrium feedback control. This setting allows us to determine for each quantity the convergence domain of the large deviation estimators using a criterion that does not require the knowledge of the probability distribution. By extracting both the asymptotic exponential decay and the subexponential prefactors, we demonstrate that singular prefactors significantly restrict the convergence characteristics. Our results provide unique insight into the approach to the asymptotic large deviation limit and underscore the pivotal role of singular prefactors.