We derive a one-parametric family of entropy functions that respect the additivity condition, and which describe effects of finiteness of statistical systems, in particular, distribution functions with long tails. This one-parametric family is different from the Tsallis entropies, and is a convex combination of the Boltzmann-Gibbs-Shannon entropy and the entropy function proposed by Burg. An ex...

The paper presents the mathematical model of computating the compessibility, thermal expansion coefficient, evaporation curve, velocity of sound and other thermophysical properties by means of statistical thermodynamics for some imortant refrigerants. The paper features all important forms of motion of molecules and atoms [translation, rotation, internal rotation, vibration], the influence of e...

Model choice plays an increasingly important role in Statistics. From a Bayesian perspective a crucial goal is to compute the marginal likelihood of the data for a given model. This however is typically a difficult task since it amounts to integrating over all model parameters. The aim of this paper is to illustrate how this may be achieved using ideas from thermodynamic integration or path sam...

We study field correlation functions for an impenetrable Bose gas with Neumann or Dirichlet boundaries. We derive the Fredholm minor determinant formulas for the correlation functions in a finite box. In the thermodynamic limit, we express the correlation functions in terms of solutions of non-linear differential equations which was introduced as the generalization of the fifth Painlevé equations.

The engineering calculation and simulation of absorption refrigeration systems require the availability of simple and efficient functions for the determination of thermodynamic property values of the operating fluid. This work presents a set of five simple and explicit functions for the determination of the vapor - liquid equilibrium properties of the ammonia-water mixture. The functions are co...

We introduce the multiplicative Ising model and prove basic properties of its thermodynamic formalism such as existence of pressure and entropies. We generalize to one-dimensional “layer-unique” Gibbs measures for which the same results can be obtained. For more general models associated to a d-dimensional multiplicative invariant potential, we prove a large deviation theorem in the uniqueness ...

An evaluation of the partial thermodynamic functions of the tantalum-oxygen system (up to O/Ta = 2.5) over the temperature range from 873 K to 3120 K is presented. The pressure-composition-temperature (p-C-T) relationship in the single-phase region of solid Ta has been investigated. The relationships for other phases where no data were available from the literature have been proposed by using t...

We study the universal thermodynamic properties of systems consisting of many coupled oscillators operating in the vicinity of a homogeneous oscillating instability. In the thermodynamic limit, the Hopf bifurcation is a dynamic critical point far from equilibrium described by a statistical field theory. We perform a perturbative renormalization group study, and show that at the critical point a...

Very accurate thermodynamic potential functions are available for fluid water, ice, seawater and humid air covering wide ranges of temperature and pressure conditions. They permit the consistent computation of all equilibrium properties as, for example, required for coupled atmosphereocean models or the analysis of observational or experimental data. With the exception of humid air, these poten...