Related papers: Notes on microstate free entropy of projections
Starting from a general classical model of many interacting particles we present a well defined step by step procedure to derive the continuum-mechanics equations of nonlinear elasticity theory with fluctuations which describe the…
This paper presents a study on the relationship between transport properties and geometric free volume for hard sphere (HS) system in dense fluid region. Firstly, a generic free volume distribution function is proposed based on recent…
We analyze a random projection method for adjacency matrices, studying its utility in representing sparse graphs. We show that these random projections retain the functionality of their underlying adjacency matrices while having extra…
We prove that the theory of open projective planes is complete and strictly stable, and infer from this that Marshall Hall's free projective planes $(\pi^n : 4 \leq n \leq \omega)$ are all elementary equivalent and that their common theory…
The paper starts with discussion of applications of cycle spaces to transportation cost. After a short survey of the known results on cycle spaces, we turn to the study of minimal projections onto cycle spaces in the corresponding…
This talk is organized as follows: First we explain some basic concepts in non-commutative probability theory in the frame of operator algebras. In Section 2, we discuss related topics in von Neumann algebras. Sections 3 and 4 contain some…
Assuming that the dominant contribution, to the entropy due to entanglement across a spherical hypersurface, comes from the near horizon degrees of freedom, we analytically derive the entropy of a free massless scalar field in Minkowski…
The present paper is meant to give a simple introduction to the problem of the connection between microscopic dynamics and statistical laws. For sake of simplicity, we mostly refer to non-dissipative dynamics, since dissipation adds…
We present a technique for calculating free-energy profiles for the nucleation of multicomponent structures that contain as many species as building blocks. We find that a key factor is the topology of the graph describing the connectivity…
Using a maximum entropy principle to assign a statistical weight to any graph, we introduce a model of random graphs with arbitrary degree distribution in the framework of standard statistical mechanics. We compute the free energy and the…
In this paper, we investigate steady two-dimensional free-surface flows of an inviscid and incompressible fluid emerging from a nozzle, falling under gravity and impinging onto a horizontal wall. More precisely, for any given atmosphere…
The ground state density matrix for a massless free field is traced over the degrees of freedom residing inside an imaginary sphere; the resulting entropy is shown to be proportional to the area (and not the volume) of the sphere. Possible…
In the context of many-fermion systems, "correlation" refers to the inadequacy of an independent-particle model. Using "free" states as archetypes of our independent-particle model, we have proposed a measure of correlation that we called…
The entropy power inequality for independent random vectors is a foundational result of information theory, with deep connections to probability and geometric functional analysis. Several extensions of the entropy power inequality have been…
We propose a free-energy based Monte-Carlo method to measure the volume of potential-energy basins in configuration space. Using this approach we can estimate the number of distinct potential-energy minima, even when this number is much too…
We develop a theory of static friction by modeling the homogeneous surfaces of contact as being composed of a regular array of compressible elastic smooth microscopic inclines. Static friction is thought of as the resistance due to having…
The first aims of this work are to endorse the advent of finitely additive set functions as equilibrium states and the possibility to replace the metric entropy by an upper semi-continuous map associated to a general variational principle.…
We prove Terao conjecture saying that the freeness is determined by the combinatorics for arrangements of 13 lines in the complex projective plane and that the property of being nearly free is combinatorial for line arrangements of up to 12…
The concept of entropy connects the number of possible configurations with the number of variables in large stochastic systems. Independent or weakly interacting variables render the number of configurations scale exponentially with the…
In its continuous version, the entropy functional measuring the information content of a given probability density may be plagued by a "measure" problem that results from improper weighting of phase space. This issue is addressed…