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arxiv: 2512.24877 · v2 · submitted 2025-12-31 · ❄️ cond-mat.stat-mech · physics.bio-ph· physics.data-an

Exact Identity Linking Entropy Production and Mutual Information

Doohyeong Cho , Hawoong Jeong This is my paper

Pith reviewed 2026-05-16 18:35 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech physics.bio-phphysics.data-an
keywords entropy productionmutual informationLangevin dynamicsstochastic thermodynamicsirreversibilitybipartite systems
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The pith

For overdamped Langevin dynamics, the entropy production rate equals four times the mutual information rate between an infinitesimal displacement and its time midpoint, plus a mean flow term.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper derives an exact identity for overdamped Langevin dynamics in which the total entropy production rate is four times the mutual information rate between an infinitesimal displacement and the position at the time midpoint, plus a mean flow term. This identity offers a forward-time characterization of irreversibility. For additive bipartite systems, it yields a decomposition of subsystem entropy production into self and interaction components via the chain rule. The self term matches apparent entropy production, while the interaction term accounts for the dissipative cost of dependence and improves learning rate bounds, as demonstrated in an application to red blood cell flickering.

Core claim

We establish an exact identity for overdamped Langevin dynamics: the total entropy production rate equals four times the mutual information rate between an infinitesimal displacement and its time midpoint, plus a mean flow term. This yields a forward-only characterization of irreversibility. As a corollary, for additive bipartite systems, the chain rule directly yields a canonical nonnegative decomposition of subsystem entropy production into self and interaction components. The self term coincides with apparent entropy production, while the interaction term captures the dissipative cost of dependence and sharpens the learning rate bound. In a proof-of-concept application to red blood cell,

What carries the argument

The exact identity that equates the total entropy production rate to four times the mutual information rate between an infinitesimal displacement and its time midpoint plus a mean flow term.

If this is right

  • This provides a forward-only characterization of irreversibility without reference to time-reversed paths.
  • For additive bipartite systems, subsystem entropy production decomposes into nonnegative self and interaction components.
  • The self component coincides with the apparent entropy production of each subsystem.
  • The interaction component quantifies the dissipative cost due to dependence between subsystems and sharpens the learning rate bound.
  • The decomposition is applied to red blood cell flickering to uncover the thermodynamic structure of mechanical irreversibility.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The identity may permit estimation of entropy production directly from forward-time trajectory data in physical experiments.
  • The bipartite decomposition could separate intrinsic dissipation from correlation-induced dissipation in a wider range of stochastic systems.
  • Testing the identity in systems with inertial dynamics would check whether the factor of four is specific to the overdamped limit.
  • This information-theoretic reformulation of entropy production might link to bounds in nonequilibrium statistical mechanics and machine learning.

Load-bearing premise

The identity is derived specifically for overdamped Langevin dynamics, so it may not hold exactly for processes with inertia or memory effects.

What would settle it

Compute the entropy production rate, the mutual information rate between displacement and midpoint, and the mean flow term in an overdamped Langevin simulation and check whether the first equals four times the second plus the third.

Figures

Figures reproduced from arXiv: 2512.24877 by Doohyeong Cho, Hawoong Jeong.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic illustration of displacement ∆ [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Physical mechanism and numerical validation of Eq. ( [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Information-theoretic EP decomposition and [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Application to OT-sensing RBC fluctuations [ [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
read the original abstract

We establish an exact identity for overdamped Langevin dynamics: the total entropy production rate equals four times the mutual information rate between an infinitesimal displacement and its time midpoint, plus a mean flow term. This yields a forward-only characterization of irreversibility. As a corollary, for additive bipartite systems, the chain rule directly yields a canonical nonnegative decomposition of subsystem entropy production into self and interaction components. The self term coincides with apparent entropy production, while the interaction term captures the dissipative cost of dependence and sharpens the learning rate bound. In a proof-of-concept application to red blood cell flickering, the decomposition reveals the thermodynamic structure of mechanical irreversibility. Overall, our results recast entropy production as a decomposable information-theoretic structure.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript claims to establish an exact identity for overdamped Langevin dynamics in which the total entropy production rate equals four times the mutual information rate between an infinitesimal displacement and its time midpoint, plus a mean flow term. This is presented as yielding a forward-only characterization of irreversibility. As a corollary, the chain rule is said to produce a canonical nonnegative decomposition of subsystem entropy production into self and interaction components for additive bipartite systems, with the self term coinciding with apparent entropy production. A proof-of-concept application to red blood cell flickering is mentioned to illustrate the thermodynamic structure of mechanical irreversibility.

Significance. If the identity and decomposition hold, the work would recast entropy production as a decomposable information-theoretic quantity, providing a forward-only view of irreversibility and a sharpened decomposition for bipartite systems that separates apparent entropy production from the dissipative cost of dependence. This could strengthen information-theoretic bounds in nonequilibrium thermodynamics and offer new analysis tools for biophysical systems, as suggested by the red blood cell example.

major comments (2)
  1. [Abstract] Abstract: The central claim of an 'exact identity' (entropy production rate = 4 × mutual information rate + mean flow term) is asserted without any derivation steps, stochastic calculus details, explicit assumptions on the overdamped Langevin process, or verification. This absence makes it impossible to assess the validity of the factor of four or the claimed exactness.
  2. [Abstract] Abstract: No definition or derivation is supplied for the mutual information rate between the infinitesimal displacement and its time midpoint, nor for the mean flow term, both of which are load-bearing for the identity and the subsequent bipartite decomposition.
minor comments (1)
  1. [Abstract] Abstract: The abstract is dense and would benefit from a brief statement of the key definitions (e.g., the precise form of the mutual information rate) to aid immediate comprehension.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their detailed review and constructive suggestions. The comments highlight the need for more clarity in the abstract regarding the derivation of the main identity. We address each point below and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The central claim of an 'exact identity' (entropy production rate = 4 × mutual information rate + mean flow term) is asserted without any derivation steps, stochastic calculus details, explicit assumptions on the overdamped Langevin process, or verification. This absence makes it impossible to assess the validity of the factor of four or the claimed exactness.

    Authors: We agree that the abstract, due to its brevity, does not include the full derivation steps or stochastic calculus details. These are provided in the main text of the manuscript, where we derive the identity using the properties of overdamped Langevin dynamics under the stated assumptions. The factor of four arises from the specific definition of the mutual information rate between the displacement and the time midpoint. We will revise the abstract to include a short reference to the derivation in the main text and mention the key assumptions. revision: yes

  2. Referee: [Abstract] Abstract: No definition or derivation is supplied for the mutual information rate between the infinitesimal displacement and its time midpoint, nor for the mean flow term, both of which are load-bearing for the identity and the subsequent bipartite decomposition.

    Authors: The definitions of the mutual information rate and the mean flow term are introduced and derived in the main body, prior to stating the identity. The abstract summarizes the result without repeating these foundational definitions. To improve accessibility, we will add brief definitions or clarifications to the abstract in the revised version. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper asserts an exact identity for overdamped Langevin dynamics equating total entropy production rate to four times a mutual information rate plus a mean flow term. No derivation steps, equations, or self-citations appear in the provided abstract, so no load-bearing reduction to inputs by construction can be exhibited. The claimed result is presented as following from the stochastic dynamics rather than being defined in terms of the information quantities or fitted to data, satisfying the criteria for a self-contained first-principles derivation with no circular steps identified.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Abstract-only review prevents full audit. The central claim rests on the domain assumption of overdamped Langevin dynamics and standard properties of mutual information and entropy production rates.

axioms (1)
  • domain assumption Dynamics obey overdamped Langevin equations
    The identity is stated to hold specifically for overdamped Langevin dynamics.

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Reference graph

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