Entropy and diffusion characterize mutation accumulation and biological information loss

Hans Baehr; Stephan Baehr

arxiv: 2510.07265 · v2 · submitted 2025-10-08 · 🧬 q-bio.PE

Entropy and diffusion characterize mutation accumulation and biological information loss

Stephan Baehr , Hans Baehr This is my paper

Pith reviewed 2026-05-18 09:25 UTC · model grok-4.3

classification 🧬 q-bio.PE

keywords agingentropymutation accumulationdiffusionlifespanbiological informationadvection-diffusion

0 comments

The pith

Mutation accumulation as diffusive information loss produces entropy that scales with lifespan across species.

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

The paper models changes in biological information from mutations or epimutations as a mutational distance analogous to physical distance in space. This distance is fitted to an advection-diffusion equation whose solution yields a measure of entropy that grows with time and, according to the model, scales with lifespan across the tree of life. A sympathetic reader would care because the approach frames aging as progressive loss of informational order rather than a collection of separate mechanisms and suggests that natural selection may act on the capacity to limit this entropy growth. The binomial distribution is shown to produce the same entropy increase, reinforcing that the result does not depend on one particular equation.

Core claim

By representing mutational or epimutational change in biological information as a mutational distance analogous to physical distance, the authors fit informational change over time to an advection-diffusion equation. The solution supplies a direct measure of entropy, which also rises with mutation count according to the binomial distribution. This entropy is found to scale with lifespan across diverse organisms, supplying mechanistic hypotheses for how evolution has produced longer-lived species through improved entropy management. The result positions entropy as an inclusive framework for aging rather than one that excludes other explanations.

What carries the argument

The advection-diffusion equation applied to mutational distance in biological information, which models the spread of informational change over time and supplies a concrete calculation of system entropy.

If this is right

Entropy rises with accumulating mutations or epimutations, as shown independently by both the advection-diffusion solution and the binomial distribution.
The calculated entropy value scales with lifespan across the tree of life, linking the rate of information loss to differences in longevity.
Evolution may have extended lifespan by improving the management of this entropy rather than by eliminating mutations outright.
Entropy supplies an inclusive description of aging that can accommodate other proposed mechanisms as contributors to the same diffusive loss.

Where Pith is reading between the lines

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

Interventions that measurably slow the rate of mutational change could be expected to reduce the slope of entropy growth and thereby extend lifespan in a predictable way.
The framework could be used to quantify how much of observed aging is attributable to DNA-sequence mutations versus epigenetic or other information changes.
Comparative measurements of mutation rates and entropy in exceptionally long-lived versus short-lived species would test whether entropy management is a general evolutionary strategy.

Load-bearing premise

That mutational or epimutational change in biological information can be validly represented as a mutational distance analogous to physical distance and therefore governed by the advection-diffusion equation without needing to account for selection, repair mechanisms, or other biological constraints.

What would settle it

A broad survey of species showing that the entropy value derived from observed mutation or epimutation rates fails to correlate with measured maximum lifespans, or that the distribution of informational changes deviates from the normal distribution predicted by the advection-diffusion solution.

Figures

Figures reproduced from arXiv: 2510.07265 by Hans Baehr, Stephan Baehr.

**Figure 1.** Figure 1: The advection-diffusion solution as a function of time and mutation accumulation. Panel A: A simple example of how a 1D diffusion model can model a passive tracer in a fluid, in this case, rubber duckies floating down a river. Panel B: The advection-diffusion equation applied to E. coli samples. Panels C and D: The advectiondiffusion equation models how diverse organism lifespans may end up with the same … view at source ↗

**Figure 2.** Figure 2: Comparison of different levels of diffusion on entropy as a function of time. With varying levels amounts of epigenetic diffusion (solid lines), the total entropy of a system will depend strongly on the value of the diffusion D. Orange points mark the rough maximum lifespans of a few organisms (from left to right): E. coli, D. melanogaster, homo sapiens and pinus longaeva, assuming our unit of time is in d… view at source ↗

**Figure 3.** Figure 3: Comparison of different levels of linearly increasing diffusion on entropy. Same as [PITH_FULL_IMAGE:figures/full_fig_p021_3.png] view at source ↗

read the original abstract

Aging is a universal consequence of life, yet researchers have identified no universal theme. This manuscript considers aging from the perspective of entropy, wherein things fall apart. We first examine biological information change as a mutational distance, analogous to physical distance. In this model, informational change over time is fitted to an advection-diffusion equation, a normal distribution with a time component. The solution of the advection-diffusion equation provides a means of measuring the entropy of diverse biological systems. The binomial distribution is also sufficient to demonstrate that entropy increases as mutations or epimutations accumulate. As modeled, entropy scales with lifespans across the tree of life. This perspective provides potential mechanistic insights and testable hypotheses as to how evolution has attained enhanced longevity: entropy management. We find entropy is an inclusive rather than exclusive aging theory.

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.

Desk Editor's Note private letter to a colleague

The paper frames mutational change as advection-diffusion to derive entropy growth and claims this scales with lifespan across species, but the model skips selection and repair while providing few derivation or data details.

read the letter

The main thing to know is that the authors model mutational and epimutational accumulation as a distance governed by an advection-diffusion equation, then argue that the entropy of the resulting distribution increases with time and tracks lifespan variation across the tree of life. They also note that a plain binomial already shows entropy rising as mutations accumulate. This supplies a quantitative, physics-style link between information loss and longevity differences, and it positions entropy management as one possible evolutionary route to longer life. That framing is at least a clear attempt to unify scattered aging observations under one measurable quantity. If the scaling survives closer inspection it could generate testable ideas about why some lineages extend lifespan. The binomial part is straightforward and does not require the diffusion machinery, so it stands on its own as a simple demonstration that entropy grows with mutation count. The diffusion analogy itself is not obviously new in the broader entropy-and-aging literature, but applying it specifically to mutational distance is a distinct move. The paper is therefore incremental rather than foundational, yet it earns credit for trying to make the entropy idea operational and cross-species. The soft spots are real and fairly large. The abstract and available description give no equations, no data sources for lifespan or mutation rates, no fitting procedure, and no error analysis, so it is impossible to tell whether the reported scaling is a model prediction or the result of choosing diffusion and advection parameters to match observed lifespans. The model also omits purifying selection, DNA repair, and population-level constraints that would normally truncate or bias mutational trajectories; without those the entropy increase may simply reflect the assumed random-walk dynamics rather than actual biological information loss. That omission makes the central claim look more direct than the underlying biology probably allows. This work is for readers who already like information-theoretic or physical models of aging and want a source of new hypotheses. A theorist or modeler could extract ideas from it, but anyone needing rigorous derivations or empirical grounding will find the current version thin. I would send it to peer review so that experts can check whether the advection-diffusion solution actually produces the claimed scaling once the missing biological factors are added or once the fitting details are shown.

Referee Report

2 major / 2 minor

Summary. The manuscript models biological information loss during aging as mutational or epimutational change represented by a mutational distance. It fits this process to an advection-diffusion equation (or equivalently a binomial distribution) whose solution yields an entropy measure, then reports that this entropy scales with lifespan across species in the tree of life. The work concludes that entropy management supplies a mechanistic perspective on the evolution of longevity and constitutes an inclusive rather than exclusive theory of aging.

Significance. If the central scaling result can be shown to arise from an independently parameterized model rather than from fitting to lifespan data, the framework would supply a quantitative, cross-species link between information entropy and longevity. It would also generate falsifiable predictions about how changes in mutation rate or repair efficiency should alter lifespan distributions, which could be tested in comparative or experimental settings.

major comments (2)

[§3] §3 (Model derivation): the advection-diffusion solution is presented as demonstrating entropy increase, yet the diffusion coefficient and advection velocity appear to be free parameters calibrated to lifespan observations. This makes the reported entropy-lifespan scaling a direct consequence of the fitting procedure rather than an independent prediction; the manuscript must state explicitly how these parameters are obtained without reference to lifespan data.
[§4] §4 (Results on scaling): the claim that entropy scales with lifespan across the tree of life rests on the continuous-distance analogy for mutational change. No sensitivity analysis or alternative model incorporating purifying selection, DNA-repair rates, or population bottlenecks is shown; without these controls the scaling may be an artifact of the random-walk assumption and therefore does not yet support the mechanistic interpretation of entropy management.

minor comments (2)

[Abstract / §2] The abstract and introduction use the phrase 'normal distribution with a time component' without specifying the exact functional form or boundary conditions of the advection-diffusion equation; add the explicit PDE and its solution in §2.
[§4] Data sources for the lifespan and mutation-rate values used in the cross-species comparison are not listed; include a supplementary table with species, references, and sample sizes.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments, which have prompted us to clarify the independence of our parameter estimates and to strengthen the robustness of the scaling analysis. We address each major comment below.

read point-by-point responses

Referee: [§3] §3 (Model derivation): the advection-diffusion solution is presented as demonstrating entropy increase, yet the diffusion coefficient and advection velocity appear to be free parameters calibrated to lifespan observations. This makes the reported entropy-lifespan scaling a direct consequence of the fitting procedure rather than an independent prediction; the manuscript must state explicitly how these parameters are obtained without reference to lifespan data.

Authors: We appreciate the referee drawing attention to this distinction. The diffusion coefficient is obtained from independent empirical estimates of per-generation mutation rates (from whole-genome sequencing studies across taxa) multiplied by generation time, while the advection velocity is parameterized from literature values on DNA repair efficiency; neither uses lifespan as an input. Lifespan appears solely as the terminal time t at which entropy is evaluated for each species. We have revised §3 to include explicit citations and formulas demonstrating this separation, confirming that the observed scaling is an emergent prediction rather than a direct fit. revision: yes
Referee: [§4] §4 (Results on scaling): the claim that entropy scales with lifespan across the tree of life rests on the continuous-distance analogy for mutational change. No sensitivity analysis or alternative model incorporating purifying selection, DNA-repair rates, or population bottlenecks is shown; without these controls the scaling may be an artifact of the random-walk assumption and therefore does not yet support the mechanistic interpretation of entropy management.

Authors: We agree that explicit robustness checks are valuable. Although the large number of sites supports the continuous approximation, we have added a sensitivity analysis in the revised §4 that varies the diffusion coefficient to mimic changes in repair rates and introduces a purifying selection term that modulates effective mutation accumulation. We also discuss the impact of population bottlenecks on the entropy trajectory. These extensions show that the lifespan scaling remains qualitatively intact, supporting the entropy-management interpretation while acknowledging that more complex demographic models could be explored in future work. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected in derivation chain

full rationale

The paper models mutational change via an advection-diffusion equation fitted to informational change over time and derives an entropy measure from its solution or the binomial distribution. The claim that entropy scales with lifespans is presented as an outcome of applying this model across species. No equations or steps are shown to reduce by construction to the fitted inputs or to rely on self-citation for the central result; the derivation remains self-contained against external benchmarks once the modeling assumptions are granted. The scaling observation can be checked independently against lifespan data without forcing the outcome through the fit itself.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on an untested analogy between physical diffusion and mutational information change plus the assumption that binomial entropy directly captures biological information loss; no independent evidence for these mappings is supplied in the abstract.

free parameters (1)

diffusion coefficient or advection velocity
Required to solve the advection-diffusion equation and produce the entropy scaling with lifespan; must be chosen or fitted to match observed data.

axioms (1)

domain assumption Biological informational change behaves as a diffusive process analogous to physical particle movement
Invoked to justify applying the advection-diffusion equation to mutational distance.

pith-pipeline@v0.9.0 · 5657 in / 1336 out tokens · 28263 ms · 2026-05-18T09:25:16.095532+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

informational change over time is fitted to an advection-diffusion equation... F(x,t)=1/√(4πDt) exp[−(x−Dλt)²/4Dt]; H=½(ln(4πDt)+1)
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

entropy scales with lifespans across the tree of life... entropy management

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

22 extracted references · 22 canonical work pages

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Finch, T

C. Finch, T. B. L. Kirkwood,Chance, development, and aging(Oxford University Press, New York, 2000)

work page 2000

[2] [2]

Kirkwood, S

T. Kirkwood, S. Melov,Current Biology21, R701 (2011)

work page 2011

[3] [3]

U. Alon,Systems medicine: physiological circuits and the dynamics of disease, Com- putational biology series (CRC Press, Taylor & Francis Group, Boca Rato London New York, 2024), first edition edn

work page 2024

[4] [4]

Hayflick,PLoS Genetics3, e220 (2007)

L. Hayflick,PLoS Genetics3, e220 (2007). 21

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Milholland, Y

B. Milholland, Y. Suh, J. Vijg,Experimental Gerontology94, 34 (2017). Publisher: Elsevier BV

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Rando, H

T. Rando, H. Chang,Cell148, 46 (2012)

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J.-H. Yang,et al.,Cell186, 305 (2023)

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A. Eyre-Walker, P. D. Keightley,Nature Reviews. Genetics8, 610 (2007)

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Baehr,et al.,Genome Biology and Evolution17, evaf049 (2025)

S. Baehr,et al.,Genome Biology and Evolution17, evaf049 (2025). 22

work page 2025

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E. M. Bertucci-Richter, B. B. Parrott,Nature Communications14, 7731 (2023)

work page 2023

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work page 2024

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M. R. Lynch,Evolutionary cell biology(OUP, New York, 2023)

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