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.

Parrondo's paradox in quantum walks with time-dependent coin operators.

We show that a Parrondo paradox can emerge in two-state quantum walks without resorting to experimentally intricate high-dimensional coins. To achieve such goal we employ a time-dependent coin operator without breaking the translation spatial invariance of the system.

Multiple transitions between normal and hyperballistic diffusion in quantum walks with time-dependent jumps.

We extend to the gamut of functional forms of the probability distribution of the time-dependent step-length a previous model dubbed Elephant Quantum Walk, which considers a uniform distribution and yields hyperballistic dynamics where the variance grows cubicly with time, σ2 ∝ t3, and a Gaussian for the position of the walker. We investigate this proposal both locally and globally with the results showing that the time-dependent interplay between interference, memory and long-range hopping leads to multiple transitions between dynamical regimes, namely ballistic → diffusive → superdiffusive → ballistic → hyperballistic for non-hermitian coin whereas the first diffusive regime is quelled for implementations using the Hadamard coin. In addition, we observe a robust asymptotic approach to maximal coin-space entanglement.

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.

Analysis of return distributions in the coherent noise model.

Return distributions of the coherent noise model are studied for the system-size-independent case. It is shown that, in this case, these distributions are in the shape of q Gaussians, which are the standard distributions obtained in nonextensive statistical mechanics. Moreover, an exact relation connecting the exponent τ of avalanche size distribution and the q value of appropriate q Gaussian has been obtained as q=(τ+2)/τ . Making use of this relation one can easily determine q parameter values of the appropriate q Gaussians a priori from one of the well-known exponents of the system. Since the coherent noise model has the advantage of producing different τ values by varying a model parameter σ , clear numerical evidences on the validity of the proposed relation have been achieved for various cases. Finally, the effect of the system size has also been analyzed and an analytical expression has been proposed, which is corroborated by the numerical results.