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arxiv: 2503.20427 · v4 · pith:Q4WKZQKQnew · submitted 2025-03-26 · ❄️ cond-mat.stat-mech

Localizing entropy production along non-equilibrium trajectories

Biswajit Das , Sreekanth K Manikandan This is my paper

Pith reviewed 2026-05-22 22:57 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech
keywords entropy productionnonequilibrium thermodynamicsdeep neural networksthermodynamic uncertainty relationdata-driven inferencestochastic thermodynamicstrajectory analysisforce field reconstruction
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The pith

Deep neural networks paired with short-time uncertainty relations localize entropy production in space and time from trajectory data.

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

The paper presents a method that uses deep neural networks to represent dissipative force fields and combines it with the short-time thermodynamic uncertainty relation to infer those fields from data. This allows the localization of fluctuating entropy production both spatially and temporally along non-equilibrium trajectories. A sympathetic reader would care because entropy production quantifies irreversibility in far-from-equilibrium systems, yet measuring it locally in complex processes has been difficult. The approach is demonstrated on various systems of interest, showing it can handle high-dimensional and time-dependent cases.

Core claim

By leveraging the flexible representation of deep neural networks within the short-time thermodynamic uncertainty relation based inference scheme, the method accurately reconstructs high-dimensional, potentially time-dependent dissipative force fields and localizes fluctuating entropy production in both space and time along nonequilibrium trajectories.

What carries the argument

The short-time thermodynamic uncertainty relation combined with deep neural network representation of force fields for inference from trajectory data.

If this is right

  • Reconstruction of dissipative forces in high dimensions without assuming specific forms.
  • Spatiotemporal localization of entropy production along individual trajectories.
  • Applicability to time-dependent force fields in complex systems.
  • Successful application to physical, chemical, and biological systems of interest.

Where Pith is reading between the lines

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

  • Could enable better analysis of experimental data in active matter or biological systems where models are incomplete.
  • Potential to integrate with other machine learning techniques for even more complex dynamics.
  • Testable by comparing inferred entropy production maps to exact calculations in simple stochastic models like Brownian particles in periodic potentials.

Load-bearing premise

The short-time thermodynamic uncertainty relation inference scheme stays accurate and stable when paired with deep neural networks for high-dimensional and time-dependent force fields.

What would settle it

Running the method on a simulated trajectory from a known system, such as an overdamped particle in a time-dependent potential, and checking if the localized entropy production matches the exact calculation from the known forces.

Figures

Figures reproduced from arXiv: 2503.20427 by Biswajit Das, Sreekanth K Manikandan.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic of entropy production inference in an active biological network model. [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. (a) Temperature profile of the [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: (b). The computed thermodynamic force field is visualised to be a strongly circulating flow, indicating a strongly irreversible state of the dynamics. On the con￾trary, the dynamics with Fmax = 40 pN and S = 0.94 shows non-oscillatory features ( [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7 [PITH_FULL_IMAGE:figures/full_fig_p014_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8 [PITH_FULL_IMAGE:figures/full_fig_p015_8.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. (a) Inferred fluctuating entropy production of the [PITH_FULL_IMAGE:figures/full_fig_p016_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Analytical and inferred time–coarse-grained entropy production rate [PITH_FULL_IMAGE:figures/full_fig_p017_11.png] view at source ↗
read the original abstract

Entropy production is a universal measure of irreversibility and energy dissipation in physical, chemical, and biological systems operating far from equilibrium. However, quantifying and spatiotemporally localising it in complex processes directly from experimental data remains a major open challenge. Here we address this issue through a data-driven approach that combines the recently developed short-time thermodynamic uncertainty relation based inference scheme with machine learning techniques. Our approach leverages the flexible function representation provided by deep neural networks to achieve accurate reconstruction of high-dimensional, potentially time-dependent dissipative force fields as well as the localization of fluctuating entropy production in both space and time along nonequilibrium trajectories. We demonstrate the versatility of the framework through applications to diverse systems of fundamental interest and experimental significance, where it successfully addresses distinct challenges in localising entropy production.

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

1 major / 1 minor

Summary. The manuscript proposes a data-driven framework that integrates the short-time thermodynamic uncertainty relation (TUR) inference scheme with deep neural networks. The method aims to reconstruct high-dimensional and potentially time-dependent dissipative force fields from trajectory data and to localize fluctuating entropy production in both space and time along nonequilibrium paths. Versatility is illustrated through applications to diverse physical, chemical, and biological systems.

Significance. If the combined TUR-DNN scheme delivers accurate force-field reconstruction and entropy-production localization without introducing uncontrolled biases, the work would provide a practical tool for quantifying irreversibility directly from experimental trajectories in high-dimensional nonequilibrium systems, an area of broad interest in statistical mechanics.

major comments (1)
  1. [Abstract (central claim) and Methods (inferred from description)] The central claim requires that the short-time TUR inference scheme remains accurate and stable when the dissipative forces are represented by a DNN approximator, especially for high-dimensional or explicitly time-dependent fields where data coverage is sparse. No error bounds, stability analysis, or verification that the DNN satisfies the implicit regularity conditions of the short-time expansion (e.g., bounded higher derivatives or exact short-time scaling) are supplied; this assumption is load-bearing for both the reconstruction and localization claims.
minor comments (1)
  1. [Abstract] The abstract would be strengthened by inclusion of at least one quantitative performance metric (e.g., reconstruction error or comparison to ground-truth entropy production) from the demonstrations.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their thoughtful assessment of our manuscript. The major comment correctly identifies that the work does not supply formal error bounds or stability analysis for the combined short-time TUR-DNN approach. We respond to this point below and indicate where a revision is feasible.

read point-by-point responses

  1. Referee: The central claim requires that the short-time TUR inference scheme remains accurate and stable when the dissipative forces are represented by a DNN approximator, especially for high-dimensional or explicitly time-dependent fields where data coverage is sparse. No error bounds, stability analysis, or verification that the DNN satisfies the implicit regularity conditions of the short-time expansion (e.g., bounded higher derivatives or exact short-time scaling) are supplied; this assumption is load-bearing for both the reconstruction and localization claims.

    Authors: We agree that the manuscript provides no rigorous error bounds, stability analysis, or explicit verification that the DNN approximator satisfies the regularity conditions (such as bounded higher derivatives) implicit in the short-time TUR expansion. The method applies the established short-time TUR inference directly, using the DNN only as a flexible function approximator for the dissipative force field, with performance assessed through numerical demonstrations on several systems. Deriving general theoretical guarantees for arbitrary DNN architectures and sparse high-dimensional data is a substantial undertaking that lies outside the scope of the present work. We will revise the manuscript to add an explicit discussion of the assumptions inherited from the short-time TUR, the empirical nature of the validation, and the potential limitations in regimes of very sparse data coverage. revision: partial

Circularity Check

0 steps flagged

Minor self-citation not load-bearing; derivation remains independent

full rationale

The abstract presents the localization method as a combination of an external short-time TUR inference scheme with DNN function approximation for force-field reconstruction. No equations or steps are shown that reduce the claimed entropy-production localization to a fitted quantity by construction, nor is there evidence of self-definitional loops or ansatz smuggling. Any self-citation of the TUR scheme is not load-bearing for the central claim, which retains independent content from the ML component. This is the normal case of a self-contained approach against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review supplies no explicit free parameters, axioms, or invented entities; the central claim rests on the unstated assumption that the short-time TUR scheme transfers to DNN-based high-dimensional inference.

pith-pipeline@v0.9.0 · 5656 in / 1060 out tokens · 44063 ms · 2026-05-22T22:57:06.389734+00:00 · methodology

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