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arXiv · 2409.19203

Idempotent approach to level-2 variational principles in Thermodynamical Formalism

A. O. Lopes·J. K. Mengue·E. R. Oliveira
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Abstract

In this work we introduce an idempotent pressure to level-2 functions and its associated density entropy. All this is related to idempotent pressure functions which is the natural concept that corresponds to the meaning of probability in the level-2 max-plus context. In this general framework the equilibrium states, maximizing the variational principle, are not unique. We investigate the connections with the general convex pressure introduced recently to level-1 functions by Bi\'{s}, Carvalho, Mendes and Varandas. Our general setting contemplates the dynamical and not dynamical framework. We also study a characterization of the density entropy in order to get an idempotent pressure invariant by dynamical systems acting on probabilities; this is therefore a level-2 result. We are able to produce idempotent pressure functions at level-2 which are invariant by the dynamics of the pushforward map via a form of Ruelle operator.

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BibTeXRIS

A. O. Lopes, J. K. Mengue, E. R. Oliveira. 2024-09-28. Idempotent approach to level-2 variational principles in Thermodynamical Formalism. https://arxiv.org/abs/2409.19203

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