Perspective: Time irreversibility in systems observed at coarse resolution

TL;DR

This paper discusses the challenges of detecting and quantifying time-reversal symmetry violations in complex systems when observations are coarse-grained or low-dimensional, emphasizing the importance of underlying assumptions.

Contribution

It highlights how coarse graining and dimensionality reduction affect the detection of time-reversal symmetry violations and stresses the need for careful assumptions to ensure physically meaningful conclusions.

Findings

Coarse graining can mask time-reversal symmetry violations.

Assumptions about microscopic dynamics are crucial for correct interpretation.

Recent advances clarify the impact of data reduction on symmetry detection.

Abstract

A broken time-reversal symmetry, i.e. broken detailed balance, is central to non-equilibrium physics and is a prerequisite for life. However, it turns out to be quite challenging to unambiguously define and quantify time-reversal symmetry (and violations thereof) in practice, that is, from observations. Measurements on complex systems have a finite resolution and generally probe low-dimensional projections of the underlying dynamics, which are well known to introduce memory. In situations where many microscopic states become "lumped" onto the same observable "state" or when introducing "reaction coordinates" to reduce the dimensionality of data, signatures of a broken time-reversal symmetry in the microscopic dynamics become distorted or masked. In this perspective we highlight why in defining and discussing time-reversal symmetry, and quantifying its violations, the precise underlying assumptions on the microscopic dynamics, the coarse graining, and further reductions, are not a technical detail. These assumptions decide whether the conclusions that are drawn are physically sound or inconsistent. We summarize recent findings in the field and reflect upon key challenges.