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Boltzmann–Gibbs disentropy of f-invariant measures

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  • da Silva, José Leonardo Esteves

Abstract

The study of invariant quantifiers is a central topic in Dynamical Systems and Ergodic Theory. This note, the Boltzmann–Gibbs Disentropy DBG, a functional that uses the Lambert function W at its kernel, is employed to describe the order (or certainty) associated with f-invariant measures. The main results of the work include: (i) It is shown that for two distinct isomorphic Bernoulli shifts, their disentropies may be different; (ii) For infinite invariant measures systems, it can happen of DBG(f)<+∞ while its entropy diverges.

Suggested Citation

  • da Silva, José Leonardo Esteves, 2026. "Boltzmann–Gibbs disentropy of f-invariant measures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 689(C).
    • Handle: RePEc:eee:phsmap:v:689:y:2026:i:c:s0378437126001895
    DOI: 10.1016/j.physa.2026.131453
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