Statistical Uncertainty Principle in Stochastic Dynamics

TL;DR

This paper derives an uncertainty principle linking statistical variations of observables and forces in stochastic dynamics, clarifying the empirical basis of the maximum entropy principle and illustrating it with a molecular motor model.

Contribution

It introduces a new uncertainty principle for statistical variations in stochastic systems, connecting data sampling limits to thermodynamic force inference.

Findings

Derived an uncertainty relation for observables and forces.

Clarified the empirical origin of the maximum entropy principle.

Applied the theory to a molecular motor model.

Abstract

Maximum entropy principle identifies forces conjugated to observables and the thermodynamic relations between them, independent upon their underlying mechanistic details. For data about state distributions or transition statistics, the principle can be derived from limit theorems of infinite data sampling. This derivation reveals its empirical origin and clarify the meaning of applying it to large but finite data. We derive an uncertainty principle for the statistical variations of the observables and the inferred forces. We use a toy model for molecular motor as an example.