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Register a new userRealization of nonequilibrium thermodynamic processes using external colored noise
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We investigate the dynamics of single microparticles immersed in water that are driven out of equilibrium in the presence of an additional external colored noise. As a case study, we trap a single polystyrene particle in water with optical tweezers and apply an external electric field with flat spectrum but a finite bandwidth of the order of kHz. The intensity of the external noise controls the amplitude of the fluctuations of the position of the particle, and therefore of its effective temperature. Here we show, in two different nonequilibrium experiments, that the fluctuations of the work done on the particle obey Crooks fluctuation theorem at the equilibrium effective temperature, given that the sampling frequency and the noise cutoff frequency are properly chosen. Our experimental setup can be therefore used to improve the design of microscopic motors towards fast and efficient devices, thus extending the frontiers of nano machinery.
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We consider a macroscopic system in contact with boundary reservoirs and/or under the action of an external field. We discuss the case in which the external forcing depends explicitly on time and drives the system from a nonequilibrium state to another one. In this case the amount of energy dissipated along the transformation becomes infinite when an unbounded time window is considered. Following the general proposal by Oono and Paniconi and using results of the macroscopic fluctuation theory, we give a natural definition of a renormalized work. We then discuss its thermodynamic relevance by showing that it satisfies a Clausius inequality and that quasi static transformations minimize the renormalized work. In addition, we connect the renormalized work to the quasi potential describing the fluctuations in the stationary nonequilibrium ensemble. The latter result provides a characterization of the quasi potential that does not involve rare fluctuations.
We extend the phase field crystal method for nonequilibrium patterning to stochastic systems with external source where transient dynamics is essential. It was shown that at short time scales the system manifests pattern selection processes. These processes are studied by means of the structure function dynamics analysis. Nonequilibrium pattern-forming transitions are analyzed by means of numerical simulations.
We introduce a software generator for a class of emph{colored} (self-correlated) and emph{non-Gaussian} noise, whose statistics and spectrum depend upon only two parameters, $q$ and $tau$. Inspired by Tsallis nonextensive formulation of statistical physics, this so-called $q$-distribution is a handy source of self-correlated noise for a large variety of applications. The $q$-noise---which tends smoothly for $q=1$ to Ornstein--Uhlenbeck noise with autocorrelation $tau$---is generated via a stochastic differential equation, using the Heun method (a second order Runge--Kutta type integration scheme). The algorithm is implemented as a stand-alone library in texttt{c++}, available as open source in the texttt{Github} repository. The noises statistics can be chosen at will, by varying only parameter $q$: it has compact support for $q<1$ (sub-Gaussian regime) and finite variance up to $q=5/3$ (supra-Gaussian regime). Once $q$ has been fixed, the noises autocorrelation can be tuned up independently by means of parameter $tau$. This software provides a tool for modeling a large variety of real-world noise types, and is suitable to study the effects of correlation and deviations from the normal distribution in systems of stochastic differential equations which may be relevant for a wide variety of technological applications, as well as for the understanding of situations of biological interest. Applications illustrating how the noise statistics affects the response of a variety of nonlinear systems are briefly discussed. In many of these examples, the systems response turns out to be optimal for some $q eq1$.
We examine the Jarzynski equality for a quenching process across the critical point of second-order phase transitions, where absolute irreversibility and the effect of finite-sampling of the initial equilibrium distribution arise on an equal footing. We consider the Ising model as a prototypical example for spontaneous symmetry breaking and take into account the finite sampling issue by introducing a tolerance parameter. For a given tolerance parameter, the deviation from the Jarzynski equality depends onthe reduced coupling constant and the system size. In this work, we show that the deviation from the Jarzynski equality exhibits a universal scaling behavior inherited from the critical scaling laws of second-order phase transitions.
A nonadditive generalization of Klimontovichs S-theorem [G. B. Bagci, Int.J. Mod. Phys. B 22, 3381 (2008)] has recently been obtained by employing Tsallis entropy. This general version allows one to study physical systems whose stationary distributions are of the inverse power law in contrast to the original S-theorem, which only allows exponential stationary distributions. The nonadditive S-theorem has been applied to the modified Van der Pol oscillator with inverse power law stationary distribution. By using nonadditive S-theorem, it is shown that the entropy decreases as the system is driven out of equilibrium, indicating self-organization in the system. The allowed values of the nonadditivity index $q$ are found to be confined to the regime (0.5,1].
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