Entropic dynamics of networks

Costa, Felipe Xavier; Pessoa, Pedro

doi:10.22191/nejcs/vol3/iss1/5

Cited by 4 publications

(1 citation statement)

References 64 publications

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“…In each of these, we were able to provide insight on the dynamics by presenting the drift velocity (57) and the equilibrium stationary states (59). Additionally, as future work, we intend to apply the dynamics developed here in the distributions found in network sciences [65]. such that they equate to dA P(A ) f (A ) − dA P(A) f (A) = dA P(A) b i…”

Section: Discussionmentioning

confidence: 97%

Entropic Dynamics on Gibbs Statistical Manifolds

Pessoa

Costa

Caticha

2021

Entropy

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Entropic dynamics is a framework in which the laws of dynamics are derived as an application of entropic methods of inference. Its successes include the derivation of quantum mechanics and quantum field theory from probabilistic principles. Here, we develop the entropic dynamics of a system, the state of which is described by a probability distribution. Thus, the dynamics unfolds on a statistical manifold that is automatically endowed by a metric structure provided by information geometry. The curvature of the manifold has a significant influence. We focus our dynamics on the statistical manifold of Gibbs distributions (also known as canonical distributions or the exponential family). The model includes an “entropic” notion of time that is tailored to the system under study; the system is its own clock. As one might expect that entropic time is intrinsically directional; there is a natural arrow of time that is led by entropic considerations. As illustrative examples, we discuss dynamics on a space of Gaussians and the discrete three-state system.

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Section: Discussionmentioning

confidence: 97%

Entropic Dynamics on Gibbs Statistical Manifolds

Pessoa

Costa

Caticha

2021

Entropy

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Entropic Dynamics Yields Reciprocal Relations

Pessoa

2021

Lecture Notes in Computer Science

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Information geometry and Bose–Einstein condensation

Pessoa

2023

Chaos: An Interdisciplinary Journal of Nonlinear Science

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It is a long held conjecture in the connection between information geometry (IG) and thermodynamics that the curvature endowed by IG diverges at phase transitions. Recent work on the IG of Bose–Einstein (BE) gases challenged this conjecture by saying that in the limit of fugacity approaching unit—where BE condensation is expected—the curvature does not diverge; rather, it converges to zero. However, as the discontinuous behavior that identifies condensation is only observed at the thermodynamic limit, a study of the IG curvature at a finite number of particles, [Formula: see text], is in order from which the thermodynamic behavior can be observed by taking the thermodynamic limit ([Formula: see text]) posteriorly. This article presents such a study. We find that for a trapped gas, as [Formula: see text] increases, the values of curvature decrease proportionally to a power of [Formula: see text], while the temperature at which the maximum value of curvature occurs approaches the usually defined critical temperature. This means that, in the thermodynamic limit, the curvature has a limited value where a phase transition is observed, contradicting the forementioned conjecture.

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Entropic dynamics of networks

Cited by 4 publications

References 64 publications

Entropic Dynamics on Gibbs Statistical Manifolds

Entropic Dynamics on Gibbs Statistical Manifolds

Entropic Dynamics Yields Reciprocal Relations

Information geometry and Bose–Einstein condensation

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