Higher-Dimensional Nonlinear Thermodynamic Formalism
نویسندگان
چکیده
We introduce a higher-dimensional version of the nonlinear thermodynamic formalism introduced by Buzzi and Leplaideur, in which potential is replaced family potentials. In particular, we establish corresponding variational principle discuss existence, characterization, number equilibrium measures for this version.
منابع مشابه
A Micro-Thermodynamic Formalism
We consider the micro-canonical ensemble of a classical Hamiltonian dynamical system, the Hamiltonian being parameter dependent and in the possible presence of other first integrals. We describe a thermodynamic formalism in which a 1st law of thermodynamics, or fundamental relation, is based upon the bulk-entropy, SΩ. Under an ergodic hypothesis, SΩ is shown to be an adiabatic invariant. Expres...
متن کاملWeighted Thermodynamic Formalism and Applications
Let (X, T ) and (Y, S) be two subshifts so that Y is a factor of X. For any asymptotically sub-additive potential Φ on X and a = (a, b) ∈ R with a > 0, b ≥ 0, we introduce the notions of a-weighted topological pressure and a-weighted equilibrium state of Φ. We setup the weighted variational principle. In the case that X, Y are full shifts with one-block factor map, we prove the uniqueness and G...
متن کاملThermodynamic Formalism of Neural Computing
Neural networks are systems of interconnected processors mimicking some of the brain functions. After a rapid overview of neural computing, the thermodynamic formalism of the learning procedure is introduced. Besides its use in introducing eecient stochas-tic learning algorithms, it gives an insight in terms of information theory. Main emphasis is given in the information restitution process ; ...
متن کاملC∗-Algebras and Thermodynamic Formalism
We show a relation of the KMS state of a certain C∗Algebra U with the Gibbs state of Thermodynamic Formalism. More precisely, we consider here the shift T : X → X acting on the Bernoulli space X = {1, 2, ..., k} and μ a Gibbs state defined by a Holder continuous potential p : X → R, and L(μ) the associated Hilbert space. Consider the C∗-Algebra U = U(μ), which is a sub-C∗-Algebra of the C∗-Alge...
متن کاملThermodynamic formalism for countable Markov shifts
We give an overview of the thermodynamic formalism for countable Markov shifts, and indicate applications to surface diffeomorphisms. 1. What is “thermodynamic formalism”? 1.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Statistical Physics
سال: 2022
ISSN: ['0022-4715', '1572-9613']
DOI: https://doi.org/10.1007/s10955-022-02916-4