Related papers: Gibbs measures on permutations over one-dimensiona…

We investigate, in a fairly general setting, the limit of large volume equilibrium Gibbs measures for elasticity type Hamiltonians with clamped boundary conditions. The existence of a quasiconvex free energy, forming the large deviations…

In this paper, using of the rigorous statement and rigorous proof the Maxwell distribution as an example, we establish estimates of the distribution depending on the parameter $N$, the number of particles. Further, we consider the problem…

Gibbs' theorem, which is originally intended for canonical ensembles with complete statistics has been generalized to open systems with incomplete statistics. As a result of this generalization, it is shown that the stationary equilibrium…

We continue our study of the scale-inhomogeneous Gaussian free field introduced in Arguin and Ouimet (2016). Firstly, we compute the limiting free energy on V_N and adapt a technique of Bovier and Kurkova (2004b) to determine the limiting…

We prove that there is only one translation-invariant Gibbsian point process w.r.t. to a chosen interaction if any of them satisfies a certain bound related to concentration-of-measure. This concentration-of-measure bound is e.g. fulfilled…

In the framework of Gibbs statistical theory, the issue of the distribution of particle sizes forming the statistical system and the moments of this distribution are considered. This task is relevant for a wide variety of applications. The…

We consider the Gibbs-measures of continuous-valued height configurations on the $d$-dimensional integer lattice in the presence a weakly disordered potential. The potential is composed of Gaussians having random location and random depth;…

Let $\Gamma $ be an infinite discrete group and $\mathsf{A}\subset \Gamma $ a nonempty finite subset. The set of permutations $\sigma $ of $\Gamma $ such that $s^{-1}\sigma (s)\in \mathsf{A}$ for every $s\in \Gamma $ can be identified with…

We consider the (scalar) gradient fields $\eta=(\eta_b)$--with $b$ denoting the nearest-neighbor edges in $\Z^2$--that are distributed according to the Gibbs measure proportional to $\texte^{-\beta H(\eta)}\nu(\textd\eta)$. Here…

We propose a definition of vorticity at inverse temperature \beta for Gibbs states in quantum XY spin systems on the lattice by testing \exp[-\beta H] on a complete set of observables ("one-point functions"). We show in particular that it…

The Gibbs Paradox is essentially a set of open questions as to how sameness of gases or fluids (or masses, more generally) are to be treated in thermodynamics and statistical mechanics. They have a variety of answers, some restricted to…

We prove existence of infinite volume Gibbs measures relative to Brownian motion. We require the pair potential W to fulfill a uniform integrability condition, but otherwise our restrictions on the potentials are relatively weak. In…

We study a broad class of local homeomorphisms and continuous potentials, proving the existence and uniqueness of weak Gibbs measures. From the Gibbs property, we show the uniqueness of equilibrium states and derive a large deviations…

In this work we study the diamagnetic properties of a perfect quantum gas in the presence of a constant magnetic field of intensity $B$. We investigate the Gibbs semigroup associated to the one particle operator at finite volume, and study…

We prove the Gibbs variational formula in terms of quantum relative entropy density that characterizes translation invariant thermal equilibrium states in quantum lattice systems. It is a natural quantum extension of the similar statement…

A random vector $X=(X_1,\ldots,X_n)$ with the $X_i$ taking values in an arbitrary measurable space $(S, \mathscr{S})$ is exchangeable if its law is the same as that of $(X_{\sigma(1)}, \ldots, X_{\sigma(n)})$ for any permutation $\sigma$.…

Particle models with finitely many types of particles are considered, both on $\mathbb{Z}^d$ and on discrete point sets of finite local complexity. Such sets include many standard examples of aperiodic order such as model sets or certain…

In this paper we present a new point of view on the mathematical foundations of statistical physics of infinite volume systems. This viewpoint is based on the newly introduced notions of transition energy function, transition energy field…

For single components fluids, vanishing isothermal compressibility implies that the mass density is constant, but the same conclusion is unknown for multicomponent fluids. Here the volume remains affected by changes of the composition. In…

We define the notion of sequential Gibbs measures, inspired by on the classical notion of Gibbs measures and recent examples from the study of non-uniform hyperbolic dynamics. Extending previous results of Kempton-Pollicott and…