Stochastic Pumps Research Articles

Singular optimal driving cycles of stochastic pumps

The investigation of optimal processes has a long history in the field of thermodynamics. It is well-known that finite-time processes which minimize dissipation often exhibit discontinuities. We use a combination of numerical and analytical approaches to study the driving cycle that maximizes the output in a simple model of a stochastic pump: a system driven out of equilibrium by a cyclic variation of external parameters. We find that this optimal solution is singular, with an infinite rate of switching between sets of parameters. The appearance of such singular solutions in thermodynamic processes is surprising, but we argue that such solutions are expected to be quite common in models whose dynamics exhibit exponential relaxation, as long as the driving period is not externally fixed and is allowed to be arbitrarily short. Our results have implications to artificial molecular motors that are driven in a cyclic manner.

Imitating nonequilibrium steady states using time-varying equilibrium force in many-body diffusive systems.

An equivalence between nonequilibrium steady states (NESS) driven by a time-independent force and stochastic pumps (SP) stirred by a time-varying conservative force is studied for general many-body diffusive systems. When the particle density and current of NESS are imitated by SP time-averaged counterparts, we prove that the entropy production rate in the SP is always greater than that of the NESS, provided that the conductivity of the particle current is concave as a function of the particle density. Searching for a SP protocol that saturates the entropy production bound reveals an unexpected connection with traffic waves, where a high density region propagates against the direction of the particle current.

Dissipation, lag, and drift in driven fluctuating systems.

This work deals with thermostated fluctuating systems subjected to driven transformations of the internal energetics. The main focus is on generally multidimensional systems with continuous configurational degrees of freedom over which overdamped Markovian fluctuations take place (diffusive regime of the motion). Mutual bounds are established between the average energy dissipation, the deviation between nonequilibrium probability density and underlying equilibrium distribution due to the system's lag, and the statistical properties of the components of the directed flow induced by the transformation itself. The directed flow is here expressed in terms of time-dependent "drift velocity" associated with the probability current in a advection-like formulation of the nonstationary Fokker-Planck equation. Consideration of the drift makes that the bounds achieved here extend the inequality derived by Vaikuntanathan and Jarzynski [Europhys. Lett. 87, 60005 (2009)EULEEJ0295-507510.1209/0295-5075/87/60005] involving only dissipation and lag. The key relations are then specified for the so-called stochastic pumps, i.e., systems that reach a periodic steady state in response of cyclic transformations and that are prototypes of nonautonomous dissipative converters of input energy into directed motion; a one-dimensional case model is adopted to illustrate the main features. Complementary results concerning bounds between the evolution rates of dissipation and lag, valid for both overdamped and underdamped dynamics, are also presented.

Mapping current fluctuations of stochastic pumps to nonequilibrium steady states.

We show that current fluctuations in a stochastic pump can be robustly mapped to fluctuations in a corresponding time-independent nonequilibrium steady state. We thus refine a recently proposed mapping so that it ensures equivalence of not only the averages, but also optimal representation of fluctuations in currents and density. Our mapping leads to a natural decomposition of the entropy production in stochastic pumps similar to the "housekeeping" heat. As a consequence of the decomposition of entropy production, the current fluctuations in weakly perturbed stochastic pumps are shown to satisfy a universal bound determined by the steady state entropy production.

Unification and new extensions of the no-pumping theorems of stochastic pumps

From molecular machines to quantum dots, a wide range of mesoscopic systems can be modeled by periodically driven Markov processes, or stochastic pumps. Currents in the stochastic pumps are delimited by an exact no-go condition called the no-pumping theorem (NPT). This letter presents a unified treatment of all the adaptations of NPT known so far, and further extends it to systems with many species of interacting particles.

No-Pumping Theorem for Many Particle Stochastic Pumps

Stochastic pumps are models of artificial molecular machines which are driven by periodic time variation of parameters, such as site and barrier energies. The no-pumping theorem states that no directed motion is generated by variation of only site or barrier energies [S. Rahav, J. Horowitz, and C. Jarzynski, Phys. Rev. Lett. 101, 140602 (2008)]. We study stochastic pumps of several interacting particles and demonstrate that the net current of particles satisfies an additional no-pumping theorem.

The Francis Pump Turbine With Stochastic Blades

In the article are introduced a special hydraulic designs of pump Francis turbines. There are compared characteristics of classical pump Francis turbine and stochastic blade pumps Francis turbine. There are introduced pump Francis turbines with inserted splitter blades in the runner and pump Francis turbines with stochastic blade cascade.

A proof by graphical construction of the no-pumping theorem of stochastic pumps

A stochastic pump is a Markov model of a mesoscopic system evolving under the control ofexternally varied parameters. In the model, the system makes random transitions among anetwork of states. For such models, a ‘no-pumping theorem’ has been obtained, whichidentifies minimal conditions for generating directed motion or currents. We provide aderivation of this result using a simple graphical construction on the network ofstates.

Extracting work from stochastic pumps

The efficiency at maximum power output of stochastic pumps, systems drivenaway from equilibrium by a periodic variation of parameters, is investigated bystudying simple models in which the driving consists of abrupt jumps of systemparameters. The models are chosen to differ by qualitative aspects of thedynamics, namely the degree of directionality and cycle control. The behaviour atmaximum power output is found to depend on the choice of parameters used tomaximize the output. For a natural choice, in which the external force and theperiod of the driving are varied to increase the power output, numerical andanalytical results suggest that the efficiency at maximum power output is at most1/2.

Directed Flow in Nonadiabatic Stochastic Pumps

We analyze the operation of a molecular machine driven by the nonadiabatic variation of external parameters. We derive a formula for the integrated flow from one configuration to another, obtain a "no-pumping theorem" for cyclic processes with thermally activated transitions, and show that in the adiabatic limit the pumped current is given by a geometric expression.

Pump fluctuation effects on parametric instabilities in plasmas

In this paper, we consider the effect of stochastic pumps on the parametric instabilities, including the pump band-width effect, the effect of the frequency mismatch and of the plasma temperature fluctuations that are induced by the fluctuations in the pump itself. Contrary to what is found in the literature, the threshold for instability can initially decrease with increasing pump band-width and reach a minimum when these effects are included. We propose a physical explanation of this minimum and point out the relationship between the thresholds for the instability of the mean energy and mean amplitude of the wave. The pump amplitude and the resulting plasma temperature fluctuations compete with the pump band-width and decrease the threshold for instability. Even for large pump band-widths, the threshold for instability for a pump with fluctuating amplitude is always lower than for the coherent one. Our general conclusion is that, in studying the effect of stochastic pumps on parametric instabilities more realistically, one has to include, in addition to the pump band-width, a number of other phenomena like imperfect frequency matching, the fluctuations induced in plasma parameters and the amplitude fluctuations of the pump itself.