On Entropy Minimization and Convergence

@article{Dostoglou2019OnEM,
  title={On Entropy Minimization and Convergence},
  author={Stamatis Dostoglou and Alexander Hughes and Jianfei Xue},
  journal={Journal of Statistical Physics},
  year={2019},
  volume={177},
  pages={485 - 505}
}
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 equals the set of averages of all probability measures absolutely continuous with respect to the standard measure on the phase space (with the exception of the measure concentrated on the empty configuration). We also investigate how the set of constrains… 
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References

SHOWING 1-10 OF 37 REFERENCES

Continuity of the temperature and derivation of the Gibbs canonical distribution in classical statistical mechanics

For a classical system of interacting particles we prove, in the microcanonical ensemble formalism of statistical mechanics, that the thermodynamic-limit entropy density is a differentiable function

Analytic and clustering properties of thermodynamic functions and distribution functions for classical lattice and continuum systems

Our most complete results concern the Ising spin system with purely ferromagnetic interactions in a magnetic fieldH (or the corresponding lattice gas model with fugacityz=const. exp(−2mHβ) wherem is

An Infinite-Dimensional Geometric Structure on the Space of all the Probability Measures Equivalent to a Given One

Let M μ be the set of all probability densities equivalent to a given reference probability measure μ. This set is thought of as the maximal regular (i.e., with strictly positive densities)

Strict convexity (“continuity”) of the pressure in lattice systems

It is shown that the pressure is a strictly convex function of the translationally invariant interactions (under certain mild restrictions on the long-range part of these interactions) for classical

The equivalence of ensembles for classical systems of particles

For systems of particles in classical phase space with standard Hamiltonian, we consider (spatially averaged) microcanonical Gibbs distributions in finite boxes. We show that infinite-volume limits

Universality of local times of killed and reflected random walks

In this note we first consider local times of random walks killed at leaving positive half-axis. We prove that the distribution of the properly rescaled local time at point $N$ conditioned on being

Variational principle for Gibbs point processes with finite range interaction

The variational principle for Gibbs point processes with general finite range interaction is proved. Namely, the Gibbs point processes are identified as the minimizers of the free excess energy

Hydrodynamical limit for a Hamiltonian system with weak noise

Starting from a general hamiltonian system with superstable pairwise potential, we construct a stochastic dynamics by adding a noise term which exchanges the momenta of nearby particles. We prolve

Graphical Models, Exponential Families, and Variational Inference

The variational approach provides a complementary alternative to Markov chain Monte Carlo as a general source of approximation methods for inference in large-scale statistical models.

Convex Functions

E. F. BECKENBACH 1. A problem of Cauchy. In 1821, Cauchy [19] proposed and solved the problem of determining the class of continuous real functions ƒ(x) which satisfy the equation (1) /(*i)+ƒ(**) = /