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Motivated by the precedent study of Ordenes-Huanca and Velazquez [JSTAT textbf{093303} (2016)], we address the study of a simple model of a pure non-neutral plasma: a system of identical non-relativistic charged particles confined under an external harmonic field with frequency $omega$. We perform the equilibrium thermo-statistical analysis in the framework of continuum approximation. This study reveals the existence of two asymptotic limits: the known Brillouin steady state at zero temperature, and the gas of harmonic oscillators in the limit of high temperatures. The non-extensive character of this model is evidenced by the associated thermodynamic limit, $Nrightarrow+infty: U/N^{7/3}=const$, which coincides with the thermodynamic limit of a self-gravitating system of non-relativistic point particles in presence of Newtonian gravitation. Afterwards, the dynamics of this model is analyzed through numerical simulations. It is verified the agreement of thermo-statistical estimations and the temporal expectation values of the same macroscopic observables. The system chaoticity is addressed via numerical computation of Lyapunov exponents in the framework of the known emph{tangent dynamics}. The temperature dependence of Lyapunov exponent $lambda$ approaches to zero in the two asymptotic limits of this model, reaching its maximum during the transit between them. The chaos of the present model is very strong, since its rate is faster than the characteristic timescale of the microscopic dynamics $tau_{dyn}=1/omega$. A qualitative analysis suggests that such a strong chaoticity cannot be explained in terms of collision events because of their respective characteristic timescales are quite different, $tau_{ch}propto tau_{dyn}/N^{1/4}$ and $tau_{coll}propto tau_{dyn}$.
We investigate a motion of a colloid in a harmonic trap driven out of equilibrium by an external non-conservative force producing a torque in the presence of a uniform magnetic field. We find that steady state exists only for a proper range of parame
We investigate the nonextensivity and the q-distribution of a relativistic gas under an external electromagnetic field. We derive a formula expression of the nonextensive parameter q based on the relativistic generalized Boltzmann equation, the relat
A microscopic definition of the thermodynamic entropy in an isolated quantum system must satisfy (i) additivity, (ii) extensivity and (iii) the second law of thermodynamics. We show that the diagonal entropy, which is the Shannon entropy in the energ
We combine the shear-transformation-zone (STZ) theory of amorphous plasticity with Edwards statistical theory of granular materials to describe shear flow in a disordered system of thermalized hard spheres. The equations of motion for this system are
Using the recently constructed covariant Ito-Langevin dynamics, we develop a covariant theory of non-equilibrium thermodynamics that is applicable to small systems with multiplicative noises and with slow variables forming curved manifolds. Assuming