The length of time's arrow

TL;DR

This paper introduces a measure of time-symmetry breaking to analyze the thermodynamic arrow of time, applying it to single molecule RNA unfolding experiments to connect time asymmetry with dissipation and free energy estimation.

Contribution

It develops a novel measure of time asymmetry based on Jensen-Shannon divergence and applies it to experimental data to explore the origins of the thermodynamic arrow of time.

Findings

Time asymmetry bounds average dissipation.

Length of time's arrow influences free energy estimation accuracy.

Time asymmetry can be quantified in single molecule experiments.

Abstract

An unresolved problem in physics is how the thermodynamic arrow of time arises from an underlying time reversible dynamics. We contribute to this issue by developing a measure of time-symmetry breaking, and by using the work fluctuation relations, we determine the time asymmetry of recent single molecule RNA unfolding experiments. We define time asymmetry as the Jensen-Shannon divergence between trajectory probability distributions of an experiment and its time-reversed conjugate. Among other interesting properties, the length of time's arrow bounds the average dissipation and determines the difficulty of accurately estimating free energy differences in nonequilibrium experiments.