Kovacs-like memory effect in athermal systems: linear response analysis

We analyse the emergence of Kovacs-like memory effects in athermal systems within the linear response regime. This is done by starting from both the master equation for the probability distribution and the equations for the physically relevant moments. The general results are applied to a general class of models with conserved momentum and non-conserved energy. Our theoretical predictions, obtained within the first Sonine approximation, show an excellent agreement with the numerical results.Comment: 18 pages, 6 figures; submitted to the special issue of the journal Entropy on "Thermodynamics and Statistical Mechanics of Small Systems

Lattice models for granular-like velocity fields: Hydrodynamic limit

A recently introduced model describing -on a 1d lattice- the velocity field of a granular fluid is discussed in detail. The dynamics of the velocity field occurs through next-neighbours inelastic collisions which conserve momentum but dissipate energy. The dynamics can be described by a stochastic equation in full phase space, or through the corresponding Master Equation for the time evolution of the probability distribution. In the hydrodynamic limit, equations for the average velocity and temperature fields with fluctuating currents are derived, which are analogous to those of granular fluids when restricted to the shear modes. Therefore, the homogeneous cooling state, with its linear instability, and other relevant regimes such as the uniform shear flow and the Couette flow states are described. The evolution in time and space of the single particle probability distribution, in all those regimes, is also discussed, showing that the local equilibrium is not valid in general. The noise for the momentum and energy currents, which are correlated, are white and Gaussian. The same is true for the noise of the energy sink, which is usually negligible

Asymmetric Stochastic Resetting: Modeling Catastrophic Events

In the classical stochastic resetting problem, a particle, moving according to some stochastic dynamics, undergoes random interruptions that bring it to a selected domain, and then, the process recommences. Hitherto, the resetting mechanism has been introduced as a symmetric reset about the preferred location. However, in nature, there are several instances where a system can only reset from certain directions, e.g., catastrophic events. Motivated by this, we consider a continuous stochastic process on the positive real line. The process is interrupted at random times occurring at a constant rate, and then, the former relocates to a value only if the current one exceeds a threshold; otherwise, it follows the trajectory defined by the underlying process without resetting. We present a general framework to obtain the exact non-equilibrium steady state of the system and the mean first passage time for the system to reach the origin. Employing this framework, we obtain the explicit solutions for two different model systems. Some of the classical results found in symmetric resetting such as the existence of an optimal resetting, are strongly modified. Finally, numerical simulations have been performed to verify the analytical findings, showing an excellent agreement.Comment: 10 pages including: main text with 6 figures and appendice

Optimal work in a harmonic trap with bounded stiffness

We apply Pontryagin's principle to drive rapidly a trapped overdamped Brownian particle in contact with a thermal bath between two equilibrium states corresponding to different trap stiffness $\kappa$. We work out the optimal time dependence $\kappa(t)$ by minimising the work performed on the particle under the non-holonomic constraint $0\leq\kappa\leq\kappa_{\max}$, an experimentally relevant situation. Several important differences arise, as compared with the case of unbounded stiffness that has been analysed in the literature. First, two arbitrary equilibrium states may not always be connected. Second, depending on the operating time $t_{\text{f}}$ and the desired compression ratio $\kappa_{\text{f}}/\kappa_{\text{\i}}$, different types of solutions emerge. Finally, the differences in the minimum value of the work brought about by the bounds may become quite large, which may have a relevant impact on the optimisation of heat engines.Comment: 16 pages, 9 figures; submitted to Physical Review

Relevance of the speed and direction of pulling in simple modular proteins

A theoretical analysis of the unfolding pathway of simple modular proteins in length- controlled pulling experiments is put forward. Within this framework, we predict the first module to unfold in a chain of identical units, emphasizing the ranges of pulling speeds in which we expect our theory to hold. These theoretical predictions are checked by means of steered molecular dynamics of a simple construct, specifically a chain composed of two coiled-coils motives, where anisotropic features are revealed. These simulations also allow us to give an estimate for the range of pulling velocities in which our theoretical approach is valid.Comment: Accepted for publication in J. Chem. Theory Comput.; only one PDF file with the main text and the supporting information (generated from a docx file

Stochastic resetting with refractory periods: pathway formulation and exact results

We look into the problem of stochastic resetting with refractory periods. The model dynamics comprises diffusive and motionless phases. The diffusive phase ends at random time instants, at which the system is reset to a given position -- where the system remains at rest for a random time interval, termed the refractory period. A pathway formulation is introduced to derive exact analytical results for the relevant observables in a broad framework, with the resetting time and the refractory period following arbitrary distributions. For the paradigmatic case of Poissonian distributions of the resetting and refractory times, in general with different characteristic rates, results are obtained in closed-form. Finally, we focus on the single-target search problem, in which the survival probability and the mean first passage time to the target can be exactly computed. Therein, we also discuss optimal strategies, which show a non-trivial dependence on the refractory period.Comment: 23 pages, 4 figure