相关论文: On the Variational Principle for Generalized Gibbs…

This paper proposes a Bayesian method for estimating the parameters of a normal distribution when only limited summary statistics (sample mean, minimum, maximum, and sample size) are available. To estimate the parameters of a normal…

For random dynamical systems, by summarizing the fundamental properties of Kifer's topological pressure we introduce the concept of random pressure functions, and define Ruelle's metric entropy for invariant measures. Employing the…

When we consider canonical average for classical discrete systems under constant composition (specifically, substitutional alloys) as a map phi from a set of many-body interatomic interactions to that of microscopic configuration in…

Quantum annealers are emerging as programmable, dynamical experimental platforms for probing strongly correlated spin systems. Yet key thermal assumptions, chiefly a Gibbs-distributed output ensemble, remain unverified in the large-scale…

We consider Gibbs distributions on permutations of a locally finite infinite set $X\subset\mathbb{R}$, where a permutation $\sigma$ of $X$ is assigned (formal) energy $\sum_{x\in X}V(\sigma(x)-x)$. This is motivated by Feynman's path…

While the thermodynamics for bosonic systems with weak $s$-wave interactions has been known for decades, a general and systematic extension to higher partial waves has not yet been reported. We provide closed-form expressions for the…

Gibbs states are familiar from statistical mechanics, yet their use is not limited to that domain. For instance, they also feature in the maximum entropy reconstruction of quantum states from incomplete measurement data. Outside the…

We prove that any asymptotics of a finite-dimensional quantum Markov processes can be formulated in the form of a generalized Jaynes principle in the discrete as well as in the continuous case. Surprisingly, we find that the open system…

We consider translation-invariant interacting particle systems on the lattice with finite local state space admitting at least one Gibbs measure as a time-stationary measure. The dynamics can be irreversible but should satisfy some mild…

A lattice system of interacting temperature loops, which is used in the Euclidean approach to describe equilibrium thermodynamic properties of an infinite system of interacting quantum particles performing anharmonic oscillations (quantum…

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,…

Gaussian measures of Gibbsian type are associated with some shell models of 3D turbulence; they are constructed by means of the energy, a conserved quantity for the 3D inviscid and unforced shell model. We prove the existence of a unique…

We propose the gentle measurement principle (GMP) as one of the principles at the foundation of quantum mechanics. It asserts that if a set of states can be distinguished with high probability, they can be distinguished by a measurement…

We derive and study quasicanonical Gibbs distribution function which is characterized by the thermostat with finite number of particles (quasithermostat). We show that this naturally leads to Tsallis nonextensive statistics and…

We construct Gibbs perturbations of the Gamma process on $\mathbbm{R}^d$, which may be used in applications to model systems of densely distributed particles. First we propose a definition of Gibbs measures over the cone of discrete Radon…

In this paper under some conditions on parameters of the Potts model with q-states on a Cayley tree of order k it is proved existence of the periodic (non translation-invariant)Gibbs measures. Also given a theorem about the number of these…

We use a weak Gibbs property and a weak form of specification to derive level-2 large deviations principles for symbolic systems equipped with a large class of reference measures. This has applications to a broad class of symbolic systems,…

Realistic equations of state valid in the whole state space of a multi-component mixture should satisfy at least three important constraints: (i) The Gibbs phase rule holds. (ii) At low densities, one can deduce a virial equation of state…

In the quantum regime, the third law of thermodynamics implies the unattainability of pure states. As shown recently, such unattainability implies that a unitary interaction between the measured system and a measuring apparatus can never…

Many Gibbs measures with mean field interactions are known to be chaotic, in the sense that any collection of $k$ particles in the $n$-particle system are asymptotically independent, as $n\to\infty$ with $k$ fixed or perhaps $k=o(n)$. This…