Evidence map›Paper›PMID 42072574›Full record

ArticleEntropy (Basel, Switzerland)2026

Dynamics, Noise, Delays and the Gibbs and Conditional Entropy.

Michael C Mackey, Marta Tyran-Kamińska

Abstract read
In one paragraph

Article in Entropy (Basel, Switzerland), 2026. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Not yet cited in PubMed.

0numbers the graph read from it
0cells of the map it votes in
0citing papers in PubMed
–field-weighted citation impact
1 · What the graph read from it

What it found

Each row is one number read from the abstract, on the scale the paper reported it, with its interval. Left of the dashed line favours the treatment, right favours the comparator. Under each row is the sentence it came from. New to these charts? A ten-minute tutorial.

The abstract states no effect estimate the extractor could read, or names no intervention and outcome on the map, so this paper lights no cell and moves no belief. It is still indexed, cited and linked below.

2 · The registry

The trial behind it

Trials whose registry record cites this paper, or whose number appears in the abstract. A trial that started after this paper was published is citing it as background, not reporting it.

Neither the registry nor the abstract names a trial number. If this is a trial report, that itself is worth knowing.

3 · Its place in the literature

Who cites it

0 citing papers in PubMed.

No citing paper in PubMed yet.

4 · The record

Corrections and comments

PubMed lists nothing against this paper. Absence here is not a guarantee, only a check that was made.

5 · Who and what money

Authors and funding

2 authors.

Michael C MackeyDepartments of Physiology, Physics & Mathematics, McGill University, 3655 Promenade Sir William Osler, Montreal, QC H3G 1Y6, Canada.ORCID 0000-0002-8524-2396
Marta Tyran-KamińskaInstitute of Mathematics, University of Silesia in Katowice, Bankowa 14, 40-007 Katowice, Poland.ORCID 0000-0002-2630-792X

Funding

No grant is acknowledged in the PubMed record.

6 · The paper itself

Abstract

In this paper we review the concepts of the Gibbs and conditional entropies and examine their dynamic behaviour when the underlying dynamics are described by ordinary differential equations or stochastic differential equations. We then go on to introduce techniques for the analogous examination when the dynamics involve delays and noise. It is found that the effects of stochastic perturbations and/or delayed dynamics may be such that the approach of the entropies to equilibrium are not necessarily monotone and are dependent on system parameters.

Indexed as

delay differential equationdensity evolutionGaussian processOrnstein–Uhlenbeck processstochastic functional differential equations

Identifiers

PMID42072574
PMCPMC13114977

What OpenQuestion holds

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Registered trials

None linked

Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.