Direct estimates of irreversibility from time series

TL;DR

This paper introduces a model-free, data-driven method to estimate the irreversibility of time series by directly analyzing trajectory data, avoiding model assumptions and accurately detecting nonequilibrium behavior.

Contribution

The authors develop a novel, model-free approach to estimate irreversibility from finite trajectory data, correcting for sampling errors and applicable to complex biological systems.

Findings

Accurately recovers zero irreversibility in systems with detailed balance.

Detects irreversibility in neural activity data from the retina.

Reveals non-Markovian dynamics in neural responses.

Abstract

The arrow of time can be quantified through the Kullback-Leibler divergence ($D_{KL}$) between the distributions of forward and reverse trajectories in a system. Many approaches to estimate this rely on specific models, but the use of incorrect models can introduce uncontrolled errors. Here, we describe a model-free method that uses trajectory data directly to estimate the evidence for irreversibility over finite windows of time. To do this we build on previous work to identify and correct for errors that arise from limited sample size. Importantly, our approach accurately recovers $D_{KL} = 0$ in systems that adhere to detailed balance, and the correct nonzero $D_{KL}$ for data generated by well understood models of nonequilibrium systems. We apply our method to trajectories of neural activity in the retina as it responds to naturalistic inputs, and find evidence of irreversibility in single neurons, emphasizing the non-Markovian character of these data. These results open new avenues for investigating how the brain represents the arrow of time.