Generalizing Planck's distribution by using the Carati-Galgani model of molecular collisions

Classical systems of coupled harmonic oscillators are studied using the Carati-Galgani model. We investigate the consequences for Einstein's conjecture by considering that the exchanges of energy, in molecular collisions, follows the L\'evy type statistics. We develop a generalization of Planck's distribution admitting that there are analogous relations in the equilibrium quantum statistical mechanics of the relations found using the nonequilibrium classical statistical mechanics approach. The generalization of Planck's law based on the nonextensive statistical mechanics formalism is compatible with the our analysis.Comment: 10 pages, 3 figure

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

Chopping Time of the FPU alpha-Model

We study, both numerically and analytically, the time needed to observe the breaking of an FPU \u3b1-chain in two or more pieces, starting from an unbroken configuration at a given temperature. It is found that such a \u201cchopping\u201d time is given by a formula that, at low temperatures, is of the Arrhenius-Kramers form, so that the chain does not break up on an observable time-scale. The result explains why the study of the FPU problem is meaningful also in the ill-posed case of the \u3b1-model

Classical microscopic theory of dispersion, emission and absorption of light in dielectrics

This paper is a continuation of a recent one in which, apparently for the first time, the existence of polaritons in ionic crystals was proven in a microscopic electrodynamic theory. This was obtained through an explicit computation of the dispersion curves. Here the main further contribution consists in studying electric susceptibility, from which the spectrum can be inferred. We show how susceptibility is obtained by the Green--Kubo methods of Hamiltonian statistical mechanics, and give for it a concrete expression in terms of time--correlation functions. As in the previous paper, here too we work in a completely classical framework, in which the electrodynamic forces acting on the charges are all taken into account, both the retarded forces and the radiation reaction ones. So, in order to apply the methods of statistical mechanics, the system has to be previously reduced to a Hamiltonian one. This is made possible in virtue of two global properties of classical electrodynamics, namely, the Wheeler--Feynman identity and the Ewald resummation properties, the proofs of which were already given for ordered system. The second contribution consists in formulating the theory in a completely general way, so that in principle it applies also to disordered systems such as glasses, or liquids or gases, provided the two general properties mentioned above continue to hold. A first step in this direction is made here by providing a completely general proof of the Wheeler--Feynman identity, which is shown to be the counterpart of a general causality property of classical electrodynamics. Finally it is shown how a line spectrum can appear at all in classical systems, as a counterpart of suitable stability properties of the motions, with a broadening due to a coexistence of chaoticity

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.Comment: 12 pages, 4 Figure