Related papers: Equilibrium states beyond specification and the Bo…
The Boltzmann and Gibbs approaches to statistical mechanics have very different definitions of equilibrium and entropy. The problems associated with this are discussed and it is suggested that they can be resolved, to produce a version of…
A realistic analysis shows that constraining a quantomechanical system produces the effective dynamics to be coupled with {\sl abelian/non-abelian gauge fields} and {\sl quantum potentials} induced by the {\sl intrinsic} and {\sl extrinsic…
When modelling driven steady states of matter, it is common practice either to choose transition rates arbitrarily, or to assume that the principle of detailed balance remains valid away from equilibrium. Neither of those practices is…
We extend the recently developed discrete geometric singular perturbation theory to the non-normally hyperbolic regime. Our primary tool is the Takens embedding theorem, which provides a means of approximating the dynamics of particular…
We prove existence and uniqueness of equilibrium states for a family of partially hyperbolic systems, with respect to Holder continuous potentials with small variation. The family comes from the projection, on the center-unstable direction,…
An unified thermodynamical framework based in the use of a generalized Massieu-Planck thermodynamic potential is proposed and a new formulation of Boltzmann-Gibbs Statistical Mechanics is established. Under this philosophy a generalization…
The defining characteristic of an exceptional point (EP) in the parameter space of a family of operators is that upon encircling the EP eigenstates are permuted. In case one encircles multiple EPs, the question arises how to properly…
We consider a one-parameter family of beam equations with Hamiltonian non-linearity in one space dimension under periodic boundary conditions. In a unified functional framework we study the long time evolution of initial data in two…
We prove the uniqueness of ground states for combined power-type nonlinear scalar field equations involving the Sobolev critical exponent and a large frequency parameter. This study is motivated by the paper [2] and aims to remove the…
We study independent and identically distributed random iterations of continuous maps defined on a connected closed subset $S$ of the Euclidean space $\mathbb{R}^{k}$. We assume the maps are monotone (with respect to a suitable partial…
We shall describe a new construction of equilibrium states for a class of partially hyperbolic systems. This generalises our construction for Gibbs measures in the uniformly hyperbolic setting. This more general setting introduces new…
In this paper, we use the thermodynamical formalism to show that there exists a unique equilibrium state $\mu_\phi$ for each expanding Thurston map $f: S^2\rightarrow S^2$ together with a real-valued H\"older continuous potential $\phi$.…
We introduce pointwise measure expansivity for bi-measurable maps. We show through examples that this notion is weaker than measure expansivity. In spite of this fact, we show that many results for measure expansive systems hold true for…
In this paper, we establish a variational principle, between the fiber Bowen's topological entropy on conditional level sets of Birkhoff average and fiber measure-theoretical entropy, for the skew product transformation driven by a uniquely…
We define a class of dynamical maps on the quasi-local algebra of a quantum spin system, which are quantum analogues of probabilistic cellular automata. We develop criteria for such a system to be ergodic, i.e., to possess a unique…
Most of the paradoxical, for the classical intuition, features of quantum theory were formulated for situations which involve a fixed number of particles. While one can now find a formulation of Bell's theorem for quantum fields, a…
We deal with countable alphabet locally compact random subshifts of finite type (the latter merely meaning that the symbol space is generated by an incidence matrix) under the absence of Big Images Property and under the absence of uniform…
We construct the Gibbs state for $\nu$-dimensional quantum crystal with site displacements from $\R^d$, $d\geq 1$, and with a one-site \textit{non-polynomial} double-well potential, which has \textit{harmonic} asymptotic growth at infinity.…
Discrete dynamical systems defined by the iteration of a polynomial map of the unit simplex to itself appear in the context of population genetic systems evolving under mutation, recombination and weak selection. Although exceptional…
We show that Rufus Bowen's Problem 32 on the classification of symbolic systems with the specification property does not admit a solution that would use concrete invariants. To this end, we construct a class of symbolic systems with the…