Carnot cycle for interacting particles in the absence of thermal noise

Abstract

A thermodynamic formalism is developed for a system of interacting particles under overdamped motion, which has been recently analyzed within the framework of nonextensive statistical mechanics. It amounts to expressing the interaction energy of the system in terms of a temperature θ, conjugated to a generalized entropy s(q), with q = 2. Since θ assumes much higher values than those of typical room temperatures T ≪ θ, the thermal noise can be neglected for this system (T/θ ≃ 0). This framework is now extended by the introduction of a work term δW which, together with the formerly defined heat contribution (δ Q = θ ds(q)), allows for the statement of a proper energy conservation law that is analogous to the first law of thermodynamics. These definitions lead to the derivation of an equation of state and to the characterization of s(q) adiabatic and θ isothermic transformations. On this basis, a Carnot cycle is constructed, whose efficiency is shown to be η = 1-(θ(2)/θ(1)), where θ(1) and θ(2) are the effective temperatures of the two isothermic transformations, with θ(1)>θ(2). The results for a generalized thermodynamic description of this system open the possibility for further physical consequences, like the realization of a thermal engine based on energy exchanges gauged by the temperature θ.

Thermodynamic framework for compact q-Gaussian distributions

“…(2.6), one results with a constant value for a; therefore, this particular choice for r 0 (ρ) yields, for high enough concentrations, r 0 → 0, so that lim ρ→∞ a(ρ) = a. As an example of this limit, one has the system of type-II superconducting vortices interacting repulsively in two dimensions (corresponding to ν = 2), for which a = 2πf 0 λ 3 [7][8][9][10][11][12][13][14][15][16][17]. The good agreement between numerical data from molecular-dynamics simulations and the analytical result of Eq.…”

“…(1.5) presents a compact support, so that the integration limits in Eqs. (1.3) and (1.4) should be replaced by finite values, ±x(t), with the cutoff of the equilibrium distribution being given by x e = lim t→∞x (t) [12][13][14][15][16][17].…”

“…Additionally, A(x) = −dφ(x)/dx corresponds to an external force derived from a confining potential φ(x), being fundamental for the approach to equilibrium, as well as for the resulting form of the probability distribution in the long-time limit. The particular case ν = 2 has been much explored recently, being shown to be directly related to a system of interacting vortices, relevant for type-II superconductors [7][8][9][10][11][12][13][14][15][16][17]; in this application, λ represents the London penetration length, and it was shown that D kT , so that thermal effects could be neglected [12]. Herein, we will be concerned with physical systems for which this approximation applies, leading to, corresponding to the NLFPE introduced in Refs.…”

Tsallis Distribution Decorated with Log-Periodic Oscillation

“…[43][44][45]. This distribution is usually used in a thermodynamical contextin which the scale parameter T is identified with the usual temperature (although such an identification cannot be solid [46][47][48][49][50]) and with a real power index n = 1/(q − 1) (or a real nonextensivity parameter q). Actually, a Tsallis distribution can be regarded as a generalization to the real power n (or q) of such well-known distributions as the Snedecor distribution (with n = (ν + 2)/2 and integer ν, which, for ν → ∞, it becomes an exponential distribution).…”

Generalized nonlinear Proca equation and its free-particle solutions

“…This proposal is motivated by recent developments cona e-mail: fdnobre@cbpf.br b e-mail: arplastino@unnoba.edu.ar cerning nonlinear extensions of the Schrödinger, Dirac, and Klein-Gordon equations [1][2][3][4][5][6][7], related to the non-extensive generalized thermostatistics [8,9]. These nonlinear equations are closely related to a family of power-law nonlinear Fokker-Planck equations that describe the spatio-temporal behavior of various physical systems and processes and have been studied intensively in recent years [10][11][12][13][14][15][16][17].…”