arXiv subjects

A. Carati

Publications and source records attributed to A. Carati.

23 records · Page 2Linked to original sources

arXiv2005

On the definition of temperature using time--averages

This paper is a natural continuation of a previous one by the author, which was concerned with the foundations of statistical thermodynamics far from equilibrium. One of the problems left open in that paper was the correct definition of temperature. In the literature, temperature is in general defined through the mean kinetic energy of the particles of a given system. In this paper, instead, temperature is defined "a la Caratheodory", the system being coupled to a heat bath, and temperature being singled out as the ``right'' integrating factor of the exchanged heat. As a byproduct, the ``right'' expression for the entropy is also obtained. In particular, in the case of a q-distributions the entropy turns out to be that of Tsallis, which we however show to be additive, at variance with what is usually maintained.

cond-mat.stat-mech↗

arXiv2004

Thermodynamics and time-average

For a dynamical system far from equilibrium, one has to deal with empirical probabilities defined through time-averages, and the main problem is then how to formulate an appropriate statistical thermodynamics. The common answer is that the standard functional expression of Boltzmann-Gibbs for the entropy should be used, the empirical probabilities being substituted for the Gibbs measure. Other functional expressions have been suggested, but apparently with no clear mechanical foundation. Here it is shown how a natural extension of the original procedure employed by Gibbs and Khinchin in defining entropy, with the only proviso of using the empirical probabilities, leads for the entropy to a functional expression which is in general different from that of Boltzmann--Gibbs. In particular, the Gibbs entropy is recovered for empirical probabilities of Poisson type, while the Tsallis entropies are recovered for a deformation of the Poisson distribution.

cond-mat.stat-mech↗

arXiv2003

Nonradiating normal modes in a classical many-body model of matter radiation interaction

We consider a classical model of matter--radiation interaction, in which the matter is represented by a system of infinitely many dipoles on a one--dimensional lattice, and the system is dealt with in the so--called dipole (i.e. linearized) approximation. We prove that there exist normal--mode solutions of the complete system, so that in particular the dipoles, though performing accelerated motions, do not radiate energy away. This comes about in virtue of an exact compensation which we prove to occur, for each dipole, between the ``radiation reaction force'' and a part of the retarded forces due to all the other dipoles. This fact corresponds to a certain identity which we name after Oseen, since it occurs that this researcher did actually propose it, already in the year 1916. We finally make a connection with a paper of Wheeler and Feynman on the foundations of electrodynamics. It turns out indeed that the Oseen identity, which we prove here in a particular model, is in fact a weak form of a general identity that such authors were assuming as an independent postulate.

physics.optics↗

arXiv2003

On the definition of temperature in FPU systems

It is usually assumed, in classical statistical mechanics, that the temperature should coincide, apart from a suitable constant factor, with the mean kinetic energy of the particles. We show that this is not the case for \FPU systems, in conditions in which energy equipartition between the modes is not attained. We find that the temperature should be rather identified with the mean value of the energy of the low frequency modes.

cond-mat.stat-mech↗

arXiv1995

A rigorous implementation of the Jeans--Landau--Teller approximation

Rigorous bounds on the rate of energy exchanges between vibrational and translational degrees of freedom are established in simple classical models of diatomic molecules. The results are in agreement with an elementary approximation introduced by Landau and Teller. The method is perturbative theory ``beyond all orders'', with diagrammatic techniques (tree expansions) to organize and manipulate terms, and look for compensations, like in recent studies on KAM theorem homoclinic splitting.

chao-dyn↗