Comment on "Exact fluctuation theorem without ensemble quantities"

TL;DR

This paper critically examines a recent claim about expressing total entropy production in measurable terms, clarifies the correct conditions for fluctuation theorems, and proposes a proper setup for their validity.

Contribution

The authors identify issues with previous work's backward protocol and provide a corrected setup and theoretical framework for fluctuation theorems under specific initial conditions.

Findings

The backward protocol must be a true time-reversal of the forward protocol.

The ratio of path probabilities does not always represent total entropy production.

Proper initial conditions are crucial for fluctuation theorem validity.

Abstract

In a recent work by Cuetara et al. (Phys. Rev. E 89, 052119 (2014)), the authors claimed that if a system is prepared under suitable initial conditions, then the total entropy production (EP) for the system and reservoirs can be expressed in terms of physically measurable quantities. However, the backward protocol used in their work is not time-reversed of the forward protocol so that the quantity obtained from the ratio of the forward and backward path probabilities is neither the total EP nor any measurable quantity. We propose a suitable setup which satisfies their pursuit. We also provide a theoretical background as to what quantity satisfies the fluctuation theorem depending on the intial conditions chosen for the forward and backward processes.