相关论文: Free analog of pressure and its Legendre transform

We introduce a wide family of stochastic processes that are obtained as sums of self-similar localized "waveforms" with multiplicative intensity in the spirit of the Richardson cascade picture of turbulence. We establish the convergence and…

The pressure and internal energy of an ultracold plasma in a state of quasi-equilibrium are evaluated using classical molecular dynamics simulations. Coulomb collapse is avoided by modeling electron-ion interactions using an attractive…

Multifractal analysis studies level sets of asymptotically defined quantities in a topological dynamical system. We consider the topological pressure function on such level sets, relating it both to the pressure on the entire phase space…

Consider two random variables contaminated by two unknown transformations. The aim of this paper is to test the equality of those transformations. Two cases are distinguished: first, the two random variables have known distributions.…

We show the robustness of the structure of Legendre transform in thermodynamics against the replacement of the standard linear average with the Kolmogorov-Nagumo nonlinear average to evaluate the expectation values of the macroscopic…

We study the relations between the averaged linear entropy production in periodically measured quantum systems and ergodic properties of their classical counterparts. Quantized linear automorphisms of the torus, both classically chaotic and…

Free fall experiments are discussed by using test masses associated to quantum states not necessarily possessing a classical counterpart. The times of flight of the Galileian experiments using classical test masses are replaced in the…

Evolution of the scale factor a(t) in Friedmann models (those with zero pressure and a constant cosmological term Lambda) is well understood, and elegantly summarized in the review of Felten and Isaacman [Rev. Mod. Phys. 58, 689 (1986)].…

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.…

A version of the classical Vieta theorem for free noncommuting variables is given. It leads to a new start in a construction of noncommutative symmetric functions

Inspired by the definition of the non-Gaussian two-parametric continuous variable analogue of an isotropic state introduced by Mi\v{s}ta et al. [Phys. Rev. A, 65, 062315 (2002); arXiv:quant-ph/0112062], we propose to take the Gaussian part…

Unlike crystalline solids or ideal gases, transport properties remain difficult to describe from a microscopic point of view in liquids, whose dynamics result from complex energetic and entropic contributions at the atomic scale. Two…

There are two natural notions of L\'evy processes in free probability: the first one has free increments with homogeneous distributions and the other has homogeneous transition probabilities. In the two cases one can associate a Nevanlinna…

Wu and Verd\'u developed a theory of almost lossless analog compression, where one imposes various regularity conditions on the compressor and the decompressor with the input signal being modelled by a (typically infinite-entropy)…

Variational inference in probabilistic graphical models aims to approximate fundamental quantities such as marginal distributions and the partition function. Popular approaches are the Bethe approximation, tree-reweighted, and other types…

It is a classical result in complex analysis that the class of functions that arise as the Cauchy transform of probability measures may be characterized entirely in terms of their analytic and asymptotic properties. Such transforms are a…

We present a new proof of an Ergodic theorem for Wide-Sense Stationary Random Processes added with a new canonical sampling theorem of mine for finite time duration signals in the frequency domain (periodograms) which is free from the…

The time variation of entropy, as an alternative to the variance, is proposed as a measure of the diffusion rate. It is shown that for linear and time-translationally invariant systems having a large-time limit for the density, at large…

Experimentally, certain degrees of freedom may appear classical because their quantum fluctuations are smaller than the experimental error associated with measuring them. An approximation to a fully quantum theory is described in which the…

We show that a probability measure is not a nontrivial free additive convolution if it puts no mass in an interval whose endpoints are atoms. The analogous results for free multiplicative convolutions are proved as well. The proofs use…