Information Exchange Fluctuation Theorem Under Coarse-Graining

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This is a fascinating and very well-conceived paper that shows that the fluctuation theorem of Sagawa and Ueda (2012) for a nonequilibrium state trajectory based on information exchange coupled to entropy production can be generalized to applicability within the context of various micro/meso coarse-grained generalizations (e.g., spatial binning, energy-based grouping, reaction coordinate projection, cluster-based course graining, and order parameter discretization), leading to a consistent nonequilibrium thermodynamic understanding/representation across various scales.  It may be interpreted in terms of compensatory thermal and configurational entropies of stochastic trajectories in phase space.  In effect, it establishes that the second law of thermodynamics is not violated for any process regardless of the degree of coarse-graining of its corresponding representation when considering the entire system and its surroundings.

I recommend publication with only minor revision.  In particular, I wonder if the author can state the degree to which any limitations on the results can be expected when systems X and Y have non-negligible interaction energy between them compared to the internal energy of X and Y.  What physical scenarios might lead to or promote such a limitation? Are there examples?  It the interaction energy term is carried along, does this result in dependence on the coarse-graining description used?  How?

Likewise, in the first sentence of the Conclusion section, perhaps the qualification should be made that “… remains invariant under coarse-graining transformations in coupled classical stochastic systems with weak interaction energies among them.”

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

This paper discusses and derives the connection between information exchange and entropy production under a coarse-grained approximation.  However, several definitions and concepts need to be clarified.

1. Please clarify what you mean by "coarse-grain" - are you referring to coarse-grained force fields or some other coarse-graining procedure?

2. Which Thermo statistical ensembles (NVT, NPT) are you discussing in your fluctuation theorem analysis?

3. The connection between your theoretical framework and Nose-Hoover thermostat implementations in molecular dynamics simulations needs to be made more explicit, and I would appreciate it. 


Page 7: 3.3 Work (about)  Fluctuation Theorem for Information Exchange

Author Response

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Reviewer 3 Report

Comments and Suggestions for Authors

In this work, the author proves two major fluctuation theorems for Markovian stochastic systems using standard methods. The conceptual significance of this work lies in its consideration of phase space coarse-graining and its impact on the fluctuation theorems concerning the time evolution of mutual information, entropy, and work. The results and derivations are scientifically sound, although I have the following suggestions for the authors:

1. Equations (3),(4),(5) are the main results of this paper, and yet they are not in Section "3. Results. " Instead, they are in Section 2 together with previous results in the literature. This makes it less clear which results are new, and could be confusing for some readers. I suggest that they be moved to the beginning of Section 3.
2. Subsection 3.1 "Theoretical Framework" contains many definitions and lengthy explanations that are either needed in or redundant with Section 2, and therefore I suggest that it be shortened and moved to Section 2.
3. The derivation of the new results relies on Eq.(12), which is the canonical result obtained by Gavin Crooks as the author has correctly referenced. However, I would recommend the author to state clearly the premises and assumptions of Crooks' result, namely, that the system is assumed to be stochastic, Markovian, and microscopically reversible.
4. In Subsection 3.3 "Work Fluctuation Theorem for Information Exchange", the author appears to have defined the "local non-equilibrium free energy" as two apparently different expressions, Eq(23) and Eq(24). In fact, Eq(23) can be derived from Eq(24) using the Feynman-Kac formula, so the definition should be Eq(24) with Eq(23) its corollary. Similarly, for the coarse-grained local non-equilibrium free energy Phi, the definition should be Eq(26). However, Eq(25) seems to be a nontrivial result which I cannot find in the references provided by the author. The author should at least comment on whether Eq(25) can also be derived using the same Feynman-Kac approach.

Author Response

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Author Response File: Author Response.pdf