Statistical Physics on the Space (x, v) for Dissipative Systems and Study of an Ensemble of Harmonic Oscillators in a Weak Linear Dissipative Medium

Abstract

We use the phase space position-velocity (x, v) to deal with the statistical properties of velocity dependent dynamical systems, like dissipative ones. Within this approach, we study the statistical properties of an ensemble of harmonic oscillators in a linear weak dissipative media. Using the Debye model of a crystal, we calculate at first order in the dissipative parameter the entropy, free energy, internal energy, equation of state and specific heat using the classical and quantum approaches. For the classical approach we found that the entropy, the equation of state, and the free energy depend on the dissipative parameter, but the internal energy and specific heat do not depend of it. For the quantum case, we found that all the thermodynamical quantities depend on this parameter.

Interacting universes and the cosmological constant

“…[7] about the questionable predictive power of the multiverse hypothesis. Of course, other schemes could be considered to tackle the collective phenomena of coupled harmonic oscillators [23][24][25][26][27][28][29][30][31]. In this respect, it is of particular interest the study of Refs.…”

About an Ambiguity Appearing on the Hamiltonian Formulation of Quantum Mechanics

“…For most of the systems (conservative or including electromagnetic interaction) seems to be that there is not problem to get a well unique Hamiltonian formulation [4]. However, when dealing with dissipative systems, it appears some problems [5,6], and it has been shown [7,8] that even there can be two different Hamiltonian bringing about the same classical behavior but different quantum behavior. In this paper, we want to point out that this type of ambiguity also appears for two conservative symmetric systems with two degrees of freedom: the harmonic oscillator and the bouncer.…”