Effects of the kinetic energy in heat for overdamped systems.

In the derivation of the thermodynamics of overdamped systems, one ignores the kinetic energy contribution since the velocity is a fast variable. In this paper, we show that the kinetic energy needs to be present in the calculation of the heat distribution to have a correct correspondence between the underdamped and overdamped cases, meaning that the velocity can not be fully ignored in the thermodynamics of these systems. We do this by investigating in detail the effect of the kinetic energy for three different systems: the harmonic potential, the logarithm potential, and an arbitrary non-isothermal process.

Large-deviation quantification of boundary conditions on the Brazil nut effect.

We present a discrete element method study of the uprising of an intruder immersed in a granular media under vibration, also known as the Brazil Nut Effect. Besides confirming granular ratcheting and convection as leading mechanisms to this odd behavior, we evince the role of the resonance on the rising of the intruder by using periodic boundary conditions (pbc) in the horizontal direction to avoid wall-induced convection. As a result, we obtain a resonance-qualitylike curve of the intruder ascent rate as a function of the external frequency, which is verified for different values of the inverse normalized gravity Γ, as well as the system size. In addition, we introduce a large deviation function analysis which displays a remarkable difference for systems with walls or pbc.

Non-Markovianity, entropy production, and Jarzynski equality.

We explore the role a non-Markovian memory kernel plays on information exchange and entropy production in the context of a external work protocol. The Jarzynski equality is shown to hold for both the harmonic and the nonharmonic models. We observe the memory function acts as an information pump, recovering part of the information lost to the thermal reservoir as a consequence of the nonequilibrium work protocol. The pumping action occurs for both the harmonic and nonharmonic cases. Unexpectedly, we found that the harmonic model does not produce entropy, regardless of the work protocol. The presence of even a small amount of nonlinearity recovers the more normal entropy producing behavior, for out-of-equilibrium protocols.

Macroscopic violation of the law of heat conduction.

We analyze a model describing an anharmonic macroscopic chain in contact with general reservoirs that follow the Lévy-Itô theorem on the Gaussian-Poissonian decomposition of the measure. We do so by considering a perturbative approach to compute the heat flux and the (canonical) temperature profile when the system reaches the steady state. This approach allows observing a macroscopic violation of the law of the heat conduction equivalent to that found for small (N=2) systems in contact with general reservoirs, which conveys the ascendency of the nature of the reservoirs over the size of the system.

Power output for a nonlinear Brownian machine.

We propose a method that makes use of the nonlinear properties of some hypothetical microscopic solid material as the working substance for a microscopic machine. The protocols used are simple (step and elliptic) and allow us to obtain the work and heat exchanged between machine and reservoirs. We calculate the work for a nonlinear single-particle machine that can be treated perturbingly. We obtain the instantaneous work and heat for the machine undergoing cycles that mimic the Carnot and multireservoir protocols. The work calculations are then extended to high values of the nonlinear parameter yielding the quasistatic limit, which is verified numerically. The model we propose is fluctuation driven and we can study in detail its thermostatistics, namely, the work distribution both per cycle and instantaneous and the corresponding fluctuation relations.

Thermostatistics of small nonlinear systems: Poissonian athermal bath.

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.

Thermostatistics of small nonlinear systems: Gaussian thermal bath.

We discuss the statistical properties of small mechanothermodynamic systems (one- and two-particle cases) subject to nonlinear coupling and in contact with standard Gaussian reservoirs. We use a method that applies averages in the Laplace-Fourier space, which relates to a generalization of the final-value theorem. The key advantage of this method lies in the possibility of eschewing the explicit computation of the propagator, traditionally required in alternative methods like path integral calculations, which is hardly obtainable in the majority of the cases. For one-particle equilibrium systems we are able to compute the instantaneous (equilibrium) probability density functions of injected and dissipated power as well as the respective large deviation functions. Our thorough calculations explicitly show that for such models nonlinearities are irrelevant in the long-term statistics, which preserve the exact same values as computed for linear cases. Actually, we verify that the thermostatistical effect of the nonlinearities is constricted to the transient towards equilibrium, since it affects the average total energy of the system. For the two-particle system we consider each element in contact with a heat reservoir, at different temperatures, and focus on the problem of heat flux between them. Contrarily to the one-particle case, in this steady state nonequilibrium model we prove that the heat flux probability density function reflects the existence of nonlinearities in the system. An important consequence of that it is the temperature dependence of the conductance, which is unobserved in linear(harmonic) models. Our results are complemented by fluctuation relations for the injected power (equilibrium case) and heat flux (nonequilibrium case).

Role of the nature of noise in the thermal conductance of mechanical systems.

Focusing on a paradigmatic small system consisting of two coupled damped oscillators, we survey the role of the Lévy-Itô nature of the noise in the thermal conductance. For white noises, we prove that the Lévy-Itô composition (Lebesgue measure) of the noise is irrelevant for the thermal conductance of a nonequilibrium linearly coupled chain, which signals the independence of mechanical and thermodynamical properties. In contrast, for the nonlinearly coupled case, the two types of properties mix and the explicit definition of the noise plays a central role.