Thermostatistics of small nonlinear systems: Poissonian athermal bath

Abstract

We extend an earlier study [W. A. M. Morgado and S. M. Duarte Queirós, Phys. Rev. E 90, 022110 (2014)PLEEE81539-375510.1103/PhysRevE.90.022110] to the case of a small system subject to nonlinear interaction and in contact with an athermal shot-noise reservoir. We first focus on steady state properties, namely, on the impact of the singular measure of the reservoir in the steady state energy. We introduce the concept of temperatures of higher order, which aim to represent the effect produced by the cumulants of the noise of order larger than 2 in the form of sources of energy of higher order and new response functions such as high-order specific heats that zero out when the system is thermal or linear. Afterwards, we study the effect of the nature of the noise in the heat and energy fluxes and determine asymptotic expressions for its large deviation functions. Finally, by analyzing the probabilistics of the injected power, we verify that the exponential form of its fluctuation relation is only asymptotically valid, whereas in the thermal case it is valid for the injected power at all times.

Langevin equation for systems with a preferred spatial direction

“…(3) singular, cf. [6]. Although in the theory of electric conductance this singularity is explained by the discrete nature of the electric charge [19], it is a rather curious aspect of Eq.…”

“…Equation (3) may be applicable to some systems, which are listed in Ref. [6] and which need a noise term of a discrete nature, e.g. systems of a small size.…”

“…[5,6] by a different non-Gaussian stochastic term, so that the extended Langevin equation for the fluctuations in systems with a preferred spatial direction would read:…”

“…To make further progress, the authors of Refs. [5,6] assumed, that this term is a Poisson process, and added it to Eq. (1), which then reads…”

“…Here P (t) is the Poisson process, also referred to as a shot noise [18,Chapter 6], which has a constant rate parameter and, in general, a variable intensity parameter [6]. The Poisson process assigns a non-zero probability only to non-negative numbers, so that the role it plays in Eq.…”