Related papers: Thermodynamic Limit for the Invariant Measures in …
We examine the minimization of information entropy for measures on the phase space of bounded domains, subject to constraints that are averages of grand canonical distributions. We describe the set of all such constraints and show that it…
For $\alpha\geq 1$, let $g:\mathbb N\to\mathbb R_+$ be given by $g(0)=0$, $g(1)=1$, $g(k)=(k/k-1)^\alpha$, $k\geq 2$. Consider the symmetric nearest neighbour zero range process on the discrete torus $\mathbb T_L$ in which a particle jumps…
We study the equivalence of ensembles for stationary measures of interacting particle systems with two conserved quantities and unbounded local state space. The main motivation is a condensation transition in the zero-range process which…
Exponential averages that appear in integral fluctuation theorems can be recast as a sum over moments of thermodynamic observables. We use two examples to show that such moment series can exhibit non-uniform convergence in certain singular…
We present general and rigorous results showing that the microcanonical and canonical ensembles are equivalent at all three levels of description considered in statistical mechanics - namely, thermodynamics, equilibrium macrostates, and…
A new method is proposed for a treatment of ideal quantum gases in the microcanonical ensemble near the thermodynamic limit. The method allows rigorous asymptotic calculations of the average number of particles and particle number…
We examine the fluctuations of the empirical density measure for the colour version of the symmetric nearest neighbour zero range particle systems in dimension one. We show that the weak limit of these fluctuations is the solution of a…
We study stochastic particle systems with stationary product measures that exhibit a condensation transition due to particle interactions or spatial inhomogeneities. We review previous work on the stationary behaviour and put it in the…
Due to the equivalence of the statistical ensembles thermostatic properties of physical systems with short-range interactions can be calculated in different ensembles leading to the same physics. In particular, the ensemble equivalence…
For studying the thermodynamic properties of systems using statistical mechanics we propose an ensemble that lies in between the familiar canonical and microcanonical ensembles. From a comparative study of these ensembles we conclude that…
Uniformity of the probability measure of phase space is considered in the framework of classical equilibrium thermodynamics. For the canonical and the grand canonical ensembles, relations are given between the phase space uniformities and…
In the thermodynamic limit the ratio of system size to thermal de Broglie wavelength tends to infinity and the volume per particle of the system is constant. Our familiar Bose-Einstein statistics is absolutely valid in the thermodynamic…
We study zero-range processes which are known to exhibit a condensation transition, where above a critical density a non-zero fraction of all particles accumulates on a single lattice site. This phenomenon has been a subject of recent…
The theorem of Shannon-McMillan-Breiman states that for every generating partition on an ergodic system, the exponential decay rate of the measure of cylinder sets equals the metric entropy almost everywhere (provided the entropy is…
We present a general framework for thermodynamic limits and its applications to a variety of models. In particular we will identify criteria such that the limits are uniform in a parameter. All results are illustrated with the example of…
We present two limit theorems, a mean ergodic and a central limit theorem, for a specific class of one-dimensional diffusion processes that depend on a small-scale parameter $\varepsilon$ and converge weakly to a homogenized diffusion…
We present a simple strategy in order to show the existence and uniqueness of the infinite volume limit of thermodynamic quantities, for a large class of mean field disordered models, as for example the Sherrington-Kirkpatrick model, and…
We prove the existence of a successful coupling for $n$ particles in the symmetric inclusion process. As a consequence we characterize the ergodic measures with finite moments, and obtain sufficient conditions for a measure to converge in…
This work explores fundamental statistical and thermodynamic properties of short-and long-range-interacting systems. The purpose of this study is twofold. Firstly, we rigorously prove that the probability distribution of arbitrary few-body…
We consider a tight binding model for localised crystalline defects with electrons in the canonical ensemble (finite electronic temperature) and nuclei positions relaxed according to the Born--Oppenheimer approximation. We prove that the…