Perspective: Time irreversibility in systems observed at coarse resolution

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.