Related papers: Ergodic optimization, zero temperature limits and …
The formalism used in describing the thermodynamics of abrupt (or first-order) phase transitions is reviewed as an application of maximum entropy inference. In this treatment, we show that the concepts of transition temperature, latent heat…
Gallagher's ergodic theorem is a result in metric number theory. It states that the approximation of real numbers by rational numbers obeys a striking 'all or nothing' behaviour. We discuss a formalisation of this result in the Lean theorem…
This paper is devoted to the study of the thermodynamic formalism for a class of real multimodal maps. This class contains, but it is larger than, Collet-Eckmann. For a map in this class, we prove existence and uniqueness of equilibrium…
We study $k$-bonacci substitutions. For each we define a renormalization operator associated to it and examine its iterates over potentials in a certain class. We also study the pressure function associated to potentials in this class and…
We summarize recent results regarding the equilibrium and non-equilibrium behavior of cold dilute atomic gases in the limit in which the two body scattering length a goes to infinity. In this limit the system is described by a Galilean…
At low temperatures the configurational phase space of a macroscopic complex system (e.g., a spin-glass) of $N\sim 10^{23}$ interacting particles may split into an exponential number $\Omega_s \sim \exp({\rm const} \times N)$ of ergodic…
Critical phenomena in non-equilibrium systems have been studied by means of a wide variety of theoretical and experimental approaches. Mode-coupling, renormalization group, complex Lie algebras and diagrammatic techniques are some of the…
We propose to study the multifractal behavior of weighted ergodic averages. Our study in this paper is concentrated on the symbolic dynamics. We introduce a thermodynamical formalism which leads to a multifractal spectrum. It is proved that…
In this article, we develop a functional-analytic framework to establish existence, uniqueness, regularity of disintegration, and statistical properties of equilibrium states for a broad class of dynamical systems, potentially discontinuous…
Various types of equilibrium processes involve electric fields. In some cases, the electrical energy appears to be negative (e.g. if the voltage is fixed by an external source). This paper explains how to derive the correct thermo-dynamic…
This paper studies ergodic properties of certain measures arising in the dynamics of holomorphic correspondences. These measures, in general, are not invariant in the classical sense of ergodic theory. We define a notion of ergodicity, and…
We first review the problem of a rigorous justification of Kubo's formula for transport coefficients in gapped extended Hamiltonian quantum systems at zero temperature. In particular, the theoretical understanding of the quantum Hall effect…
It is now well established that there is no lower bound for the energy dissipated during a computation. The relevance of the zero-energy limit is unclear, however, because it entails computations that are unreliable or infinitely slow, or…
The theory of ergodic optimization for distance-expanding maps is extended to Gauss's continued fraction map. Since the set of invariant probability measures is not weak$^*$ closed, we establish a characterisation of the closure of this…
The thermodynamical model of visco-elastic deformable solids at finite strains is formulated in a fully Eulerian way in rates. Also effects of thermal expansion or buoyancy due to evolving mass density in a gravity field are covered. The…
We investigate the possibility of introducing the temperature to the one dimensional Sznajd model and propose a natural extension of the original model by including other types of interactions. We characterise different kinds of equilibria…
Let $T:X\to X $ and $S:Y \to Y$ be continuous maps defined on compact sets. Let $$\varphi_i(\mu,\nu)=\int_{X \times Y} A_i(x,y) d\mu(x) d\nu(y)\;\;{for} \;\; i=1,2,$$ where $\mu$ is $T$-invariant and $\nu$ is $S$-invariant, be pay-off…
In this paper we study the convergence of the max-consensus protocol. Tropical algebra is used to formulate the problem. Necessary and sufficient conditions for convergence of the max-consensus protocol over fixed as well as switching…
In most studies for the quantification of the third thermodynamic law, the minimum temperature which can be achieved with a long but finite-time process scales as a negative power of the process duration. In this article, we use our recent…
We present a survey of ergodic theorems for actions of algebraic and arithmetic groups recently established by the authors, as well as some of their applications. Our approach is based on spectral methods employing the unitary…