Related papers: Billiards, Invariant Measures, and Equilibrium The…
This paper derives a density matrix of the steady-state statistical mechanics compatible with the steady-state thermodynamics proposed by Oono and Paniconi [Prog. Theor. Phys. Suppl. {\bf 130}, 29 (1998)]. To this end, we adopt three…
We consider equations describing a barotropic inviscid flow in a channel with topography effects and beta-plane approximation of Coriolis force, in which a large-scale mean flow interacts with smaller scales. Gibbsian measures associated to…
Gibbs random fields play an important role in statistics, however, the resulting likelihood is typically unavailable due to an intractable normalizing constant. Composite likelihoods offer a principled means to construct useful…
This work lies at the intersection of Gibbs models and hyperuniform point processes. Classical Gibbs models, whether defined on lattices or in continuous space, provide flexible tools to describe interacting particle systems but are…
We consider a gas whose each particle is characterised by a pair $(x,v_x)$ with the position $x\in \mathbb R^d$ and the velocity $v_x\in \mathbb R^d_0= \mathbb R^d\setminus \{0\}$. We define Gibbs measures on the cone of vector-valued…
This thesis consists of two separate parts: in each we study the stability under small perturbations of certain probability models in different contexts. In the first, we study small random perturbations of a deterministic dynamical system…
A thermodynamic-like formalism is developed for superstatistical systems based on conditional entropies. This theory takes into account large-scale variations of intensive variables of systems in nonequilibrium stationary states. Ordinary…
A simple relation is developed between elastic collisions of freely-moving point particles in one dimension and a corresponding billiard system. For two particles with masses m_1 and m_2 on the half-line x>0 that approach an elastic barrier…
A definition for elliptical tempered stable distribution, based on the characteristic function, have been explained which involve a unique spectral measure. This definition provides a framework for creating a connection between infinite…
We review our investigations on Gibbs measures relative to Brownian motion, in particular the existence of such measures and their path properties, uniqueness, resp. non-uniqueness. For the case when the energy only depends on increments,…
Energies and equilibrium equations for thin elastic plates are discussed, with emphasis on several issues pertinent to recent approaches in soft condensed matter. Consequences of choice of basis, choice of invariant strain measures, and of…
Simple application of the Einstein model combined with the elastic description of solid state is developed. The frequency of quantum oscillators has been assumed as volume dependent and, furthermore, elastic energy terms of static character…
Nonadditive Tsallis $q$-statistics has successfully been applied for a plethora of systems in natural sciences and other branches of knowledge. Nevertheless, its foundations have been severely criticised by some authors based on the…
It is shown that power law phase space distributions describe marginally stable Gibbsian equilibria far from thermal equilibrium which are expected to occur in collisionless plasmas containing fully developed quasi-stationary turbulence.…
The properties of statistical ensembles with abelian charges close to the thermodynamic limit are discussed. The finite volume corrections to the probability distributions and particle density moments are calculated. Results are obtained…
Macroscopic thermodynamics, via the weak coupling approximation, assumes that the equi?librium properties of a system are not affected by interactions with its environment. However, this assumption may not hold for quantum systems, where…
It has been argued in [EPL {\bf 90} (2010) 50004], entitled {\it Essential discreteness in generalized thermostatistics with non-logarithmic entropy}, that "continuous Hamiltonian systems with long-range interactions and the so-called…
A ray-tracing method inspired by ergodic billiards is used to estimate the theoretically best decision rule for a set of linear separable examples. While the Bayes-optimum requires a majority decision over all Perceptrons separating the…
We discuss the relationship between discrete-time processes (chains) and one-dimensional Gibbs measures. We consider finite-alphabet (finite-spin) systems, possibly with a grammar (exclusion rule). We establish conditions for a stochastic…
We explain the Curie Weiss model in Statistical Mechanics within the Ergodic viewpoint. More precisely, we simultaneously define in $\{-1,+1\}^{\mathbb{N}}$, on the one hand a generalized Curie Weiss model within the Statistical Mechanics…