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arxiv: 2605.13556 · v1 · submitted 2026-05-13 · ❄️ cond-mat.stat-mech

Recognition: 2 theorem links

· Lean Theorem

Emergence of information interference in stochastic systems with non-diagonal noise and switching environments

Andrea Marchetti , Daniel Maria Busiello , Giorgio Nicoletti
Authors on Pith no claims yet

Pith reviewed 2026-05-14 18:01 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech
keywords mutual informationinformation interferencenon-diagonal noisestochastic switchinglinearized systemshydrodynamic interactionschemical reaction networks
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The pith

Stochastic systems with non-diagonal noise and switching environments develop non-additive mutual information.

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

The paper shows that in linearized stochastic systems, the presence of both non-diagonal noise and stochastically switching environments produces interference in the mutual information, so that the total cannot be written as the sum of separate contributions from deterministic couplings, noise anisotropy, and environmental changes. A reader would care because real systems ranging from hydrodynamically coupled colloids to chemical reaction networks routinely combine correlated noise with varying conditions, making the origins of statistical dependencies between variables a practical question. The work isolates a static interference term that appears when deterministic coupling acts together with anisotropic noise and a dynamic term that appears when internal relaxation processes interact with the switches, then illustrates the effects in concrete physical models.

Core claim

In linearized Langevin dynamics with a non-diagonal diffusion matrix and Markovian switching between environments, the mutual information rate acquires extra cross terms. These static terms originate from the joint action of deterministic forces and noise correlations, while dynamic terms originate from the coupling between relaxation timescales and the switching process. The result is that mutual information is non-additive and cannot be decomposed into independent pieces.

What carries the argument

Information interference, the non-additive excess in mutual information that appears only when deterministic coupling, noise anisotropy, and environmental switching are all present simultaneously.

Load-bearing premise

The derivations assume linear dynamics together with particular forms of the noise matrix and the switching process.

What would settle it

Numerically integrate a two-variable linear system with off-diagonal noise entries and periodic environmental switching, compute the mutual information rate, subtract the separately calculated contributions from coupling alone, noise alone, and switching alone, and check whether a nonzero residual remains that matches the predicted interference expressions.

Figures

Figures reproduced from arXiv: 2605.13556 by Andrea Marchetti, Daniel Maria Busiello, Giorgio Nicoletti.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) Total MI between two DOFs [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a) Two identical particles ( [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (a) A chemical system with three species [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
read the original abstract

Stochastic forces in natural systems are rarely isotropic. From hydrodynamically coupled colloids to chemical reaction networks, noise contributions are inherently correlated. Together with internal interactions and changing environments, they shape the dependencies between the degrees of freedom of real-world systems, as quantified by their mutual information. In this work, we focus on linearized stochastic systems with both non-diagonal noise matrices and stochastically switching environments. We study how their presence leads to the emergence of information interference, so that the total mutual information cannot be decomposed as the sum of the contributions from deterministic interactions, noise anisotropy, and environmental switching alone. We identify two distinct sources of information interference: a static term, arising from the simultaneous presence of deterministic coupling and noise anisotropy; and a dynamic term, emerging from the interplay between internal processes and environmental switches. We then apply this framework to different physical systems. In the presence of switching temperatures, the mutual information disentangles exactly into internal and environmental contributions. When the noise anisotropy arises instead from hydrodynamic interactions, we find that the presence of a shared fluid can either mask or enhance the information stemming from a non-conservative force depending on its degree of non-reciprocity. Finally, in a fuel-driven chemical reaction network, we show that information interference is controlled by the non-equilibrium driving. These results establish a general information-theoretic perspective on how anisotropic noise and environmental variability shape statistical dependencies in stochastic systems.

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

0 major / 3 minor

Summary. The manuscript develops an information-theoretic framework for linearized stochastic systems subject to non-diagonal noise and stochastically switching environments. It shows that the stationary mutual information cannot be decomposed additively into separate contributions from deterministic coupling, noise anisotropy, and environmental switching; instead, two interference terms appear—a static term generated by the joint presence of coupling and anisotropic noise via the Lyapunov equation for the covariance, and a dynamic term arising from the modulation of effective drift and diffusion by the switches. The framework is applied to three physical examples: temperature switching (where mutual information factors exactly), hydrodynamic interactions (where a shared fluid can mask or enhance non-reciprocal-force information), and a fuel-driven chemical reaction network (where interference is tuned by non-equilibrium driving).

Significance. If the central decomposition holds, the work supplies a concrete, computable route to quantify how correlated fluctuations and environmental variability generate non-additive statistical dependencies. The explicit separation into static and dynamic interference terms, together with the exact factorization in the temperature-switching case and the parameter-free predictions in the hydrodynamic example, are genuine strengths that could be useful for non-equilibrium thermodynamics and stochastic modeling of colloidal, chemical, and biological systems.

minor comments (3)
  1. [§4.2] §4.2, after Eq. (19): the statement that the hydrodynamic case yields a 'parameter-free' enhancement factor should be accompanied by an explicit expression for the factor in terms of the mobility matrix and the non-reciprocity parameter; the current wording leaves the reader to reconstruct it from the Lyapunov solution.
  2. [Figure 3] Figure 3 caption: the color scale for the mutual-information surface is not labeled with units or a numerical range; this makes quantitative comparison with the analytic curves in panel (b) difficult.
  3. [§5] §5, paragraph 2: the claim that 'information interference is controlled by the non-equilibrium driving' would be strengthened by a brief remark on whether the same control persists when the switching rates become comparable to the internal relaxation rates.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive and accurate summary of our manuscript, which correctly identifies the emergence of static and dynamic information interference terms that prevent additive decomposition of mutual information in systems with non-diagonal noise and switching environments. We appreciate the recognition of the framework's applicability to the three physical examples and the strengths highlighted in the significance assessment. The recommendation for minor revision is noted, and we will prepare a revised version accordingly.

Circularity Check

0 steps flagged

Derivation self-contained; no circular steps identified

full rationale

The central derivation computes stationary covariance via the Lyapunov equation for linearized systems with non-diagonal noise and stochastic switching, then obtains mutual information from the standard log-det formula on that covariance. The static interference term follows directly from cross terms induced by simultaneous coupling and anisotropy; the dynamic term follows from switching modulating the effective drift/diffusion. No step renames a fitted quantity as a prediction, imports uniqueness via self-citation, or smuggles an ansatz; the framework is fully determined by the stated model equations inside the linear regime.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The framework rests on standard linearized stochastic differential equations and mutual information definitions from information theory, with the new decomposition introduced in the paper.

axioms (1)
  • domain assumption Linearized stochastic dynamics around a reference state
    The paper explicitly focuses on linearized stochastic systems.

pith-pipeline@v0.9.0 · 5557 in / 1156 out tokens · 54744 ms · 2026-05-14T18:01:05.595473+00:00 · methodology

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Reference graph

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    Slow-jump limit Here, we give mathematical ground for the decomposi- tion introduced in Eq. (15) for the limit case of a slowly switching environment (τjumps ≫τ). In this slow-jump limit, the timescale separation so- lution givesp i(x, t)≃π i(t)P st i (x) [52–54], whereπ i(t) obeys the master equation ˙πi(t) =τ jumps X j h Wij πj(t)−W ji πi(t) i (17) whil...

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    Fast-jump limit Here, we briefly comment on the other limit case of a fast switching environment (τjumps ≪τ), where the stochas- tic variables effectively experience the environment as averaged over its stationary distribution. The timescale separation limit givesp i(x, t)≃π st i P(x, t) [31, 53], where πst i is the stationary probability of the jump proc...

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