Related papers: Thermodynamic formalism for correspondences
A new formulation of the thermodynamic field theory (TFT) is presented. In this new version, one of the basic restriction in the old theory, namely a closed-form solution for the thermodynamic field strength, has been removed. In addition,…
We study thermodynamic formalism for topologically transitive partially hyperbolic systems in which the center-stable bundle satisfies a bounded expansion property, and show that every potential function satisfying the Bowen property has a…
In this paper we study the ergodic theory of a robust non-uniformly expanding maps where no Markov assumption is required. We prove that the topological pressure is differentiable as a function of the dynamics and analytic with respect to…
This study presents a new turbulence model for isothermal compressible flows. The model is derived by combining the Favre averaging and the Conservation-dissipation formalism -- a newly developed thermodynamics theory. The latter provides a…
Based on previous works, analytical calculational procedures for dealing with the strongly interacting fermions ground state are further developed through a medium dependent potential in terms of the Bethe-Peierls contact interaction model.…
We develop a quenched thermodynamic formalism for random dynamical systems generated by countably branched, piecewise-monotone mappings of the interval that satisfy a random covering condition. Given a random contracting potential $\varphi$…
This paper is concerned with modeling the polarization process in ferroelectric media. We develop a thermodynamically consistent model, based on phenomenological descriptions of free energy as well as switching and saturation conditions in…
We introduce the coherent-incoherent correspondence as a framework for deriving quantum thermodynamic uncertainty relations under continuous measurement in Lindblad dynamics. The coherent-incoherent correspondence establishes a mapping…
Expanding Thurston maps were introduced by M. Bonk and D. Meyer with motivation from complex dynamics and Cannon's conjecture from geometric group theory via Sullivan's dictionary. In this paper, we introduce subsystems of expanding…
We define a nonlinear thermodynamical formalism which translates into dynamical system theory the statistical mechanics of generalized mean-field models, extending investigation of the quadratic case by Leplaideur and Watbled. Under…
We introduce the multiplicative Ising model and prove basic properties of its thermodynamic formalism such as existence of pressure and entropies. We generalize to one-dimensional "layer-unique" Gibbs measures for which the same results can…
A classical result in thermodynamic formalism is that for uniformly hyperbolic systems, every H\"older continuous potential has a unique equilibrium state. One proof of this fact is due to Rufus Bowen and uses the fact that such systems…
We develop a new method, based on pluripotential theory, to study the transfer (Perron-Frobenius) operator induced on $\mathbb P^k = \mathbb P^k (\mathbb C)$ by a holomorphic endomorphism and a suitable continuous weight. This method allows…
A variational principle is further developed for out of equilibrium dynamical systems by using the concept of maximum entropy. With this new formulation it is obtained a set of two first-order differential equations, revealing the same…
A novel geometric formalism for statistical estimation is applied here to the canonical distribution of classical statistical mechanics. In this scheme thermodynamic states, or equivalently, statistical mechanical states, can be…
The thermodynamic formalism allows one to access the chaotic properties of equilibrium and out-of-equilibrium systems, by deriving those from a dynamical partition function. The definition that has been given for this partition function…
We elucidate that the diffusive systems, which are widely found in nature, can be a new platform of the bulk-edge correspondence, a representative topological phenomenon. Using a discretized diffusion equation, we demonstrate the emergence…
The variational method is very important in mathematical and theoretical physics because it allows us to describe the natural systems by physical quantities independently from the frame of reference used. A global and statistical approach…
We show that classical thermodynamics has a formulation in terms of Hamilton-Jacobi theory, analogous to mechanics. Even though the thermodynamic variables come in conjugate pairs such as pressure/volume or temperature/entropy, the phase…
The Thermodynamic Formalism provides a rigorous mathematical framework to study quantitative and qualitative aspects of dynamical systems. At its core there is a variational principle corresponding, in its simplest form, to the Maximum…