Classical small systems coupled to finite baths

Abstract

We have studied the properties of a classical N S -body system coupled to a bath containing N Bbody harmonic oscillators, employing an (N S + N B ) model which is different from most of the existing models with N S = 1. We have performed simulations for N S -oscillator systems, solving 2(N S + N B ) first-order differential equations with N S ≃ 1 − 10 and N B ≃ 10 − 1000, in order to calculate the time-dependent energy exchange between the system and the bath. The calculated energy in the system rapidly changes while its envelope has a much slower time dependence.Detailed calculations of the stationary energy distribution of the system f S (u) (u: an energy per particle in the system) have shown that its properties are mainly determined by N S but weakly depend on N B . The calculated f S (u) is analyzed with the use of the Γ and q-Γ distributions: the latter is derived with the superstatistical approach (SSA) and microcanonical approach (MCA) to the nonextensive statistics, where q stands for the entropic index. Based on analyses of our simulation results, a critical comparison is made between the SSA and MCA. Simulations have been performed also for the N S -body ideal-gas system. The effect of the coupling between oscillators in the bath has been examined by additional (N S + N B ) models which include baths consisting of coupled linear chains with periodic and fixed-end boundary conditions.

Tsallis power laws and finite baths with negative heat capacity

“…A related work along this direction is the one by Hasegawa [25], who notes that the nonextensivity index q emerging from the classical finite baths depends mainly on the number of particles in the system and only weakly on the bath degrees of freedom. If the finite baths would be the genuine sources of the Tsallis distributions, the finite heat capacity of the bath should have an explicit q dependence that would be affected by the bath degrees of freedom as usual.…”

Specific heat anomalies of small quantum systems subjected to finite baths

“…IV is devoted to our conclusion. is subjected to an N B -body bath (H B ) by the interaction (H I ) [13]. The total Hamiltonian is assumed to be given by…”

“…The (1 + 1) model From Eqs. (1)- (4), the Hamiltonian for the case of N S = N B = 1 is given by [13] …”

Noncanonical statistics of a finite quantum system with non-negligible system-bath coupling

“…However, if the system only interacts with a small heat bath with finite degrees of freedom, the system-bath interaction cannot be ignored. The properties of such finite system recently intrigue a lot of attentions from the aspects of both experiments [1,2] and theories [3][4][5][6][7][8][9][10][11].…”