Stochastic thermodynamics for Ising chain and symmetric exclusion process

We verify the finite time fluctuation theorem for a linear Ising chain at its ends in contact with heat reservoirs. Analytic results are derived for a chain consisting of only two spins. The system can be mapped onto a model for particle transport, namely the symmetric exclusion process, in contact with thermal and particle reservoirs. We modify the symmetric exclusion process to represent a thermal engine and reproduce universal features of the efficiency at maximum power

Extracting chemical energy by growing disorder: Efficiency at maximum power

We consider the efficiency of chemical energy extraction from the environment by the growth of a copolymer made of two constituent units in the entropy-driven regime. We show that the thermodynamic nonlinearity associated with the information processing aspect is responsible for a branching of the system properties such as power, speed of growth, entropy production, and efficiency, with varying affinity. The standard linear thermodynamics argument which predicts an efficiency of 1/2 at maximum power is inappropriate because the regime of maximum power is located either outside of the linear regime or on a separate bifurcated branch, and because the usual thermodynamic force is not the natural variable for this optimization.Comment: 6 pages, 4 figure

Optimal search strategies of space-time coupled random walkers with finite lifetimes

We present a simple paradigm for detection of an immobile target by a space-time coupled random walker with a finite lifetime. The motion of the walker is characterized by linear displacements at a fixed speed and exponentially distributed duration, interrupted by random changes in the direction of motion and resumption of motion in the new direction with the same speed. We call these walkers "mortal creepers". A mortal creeper may die at any time during its motion according to an exponential decay law characterized by a finite mean death rate $\omega_m$. While still alive, the creeper has a finite mean frequency $\omega$ of change of the direction of motion. In particular, we consider the efficiency of the target search process, characterized by the probability that the creeper will eventually detect the target. Analytic results confirmed by numerical results show that there is an $\omega_m$-dependent optimal frequency $\omega=\omega_{opt}$ that maximizes the probability of eventual target detection. We work primarily in one-dimensional ($d=1$) domains and examine the role of initial conditions and of finite domain sizes. Numerical results in $d=2$ domains confirm the existence of an optimal frequency of change of direction, thereby suggesting that the observed effects are robust to changes in dimensionality. In the $d=1$ case, explicit expressions for the probability of target detection in the long time limit are given. In the case of an infinite domain, we compute the detection probability for arbitrary times and study its early- and late-time behavior. We further consider the survival probability of the target in the presence of many independent creepers beginning their motion at the same location and at the same time. We also consider a version of the standard "target problem" in which many creepers start at random locations at the same time.Comment: 18 pages, 7 figures. The title has been changed with respect to the one in the previous versio

Synchronization of globally coupled two-state stochastic oscillators with a state dependent refractory period

We present a model of identical coupled two-state stochastic units each of which in isolation is governed by a fixed refractory period. The nonlinear coupling between units directly affects the refractory period, which now depends on the global state of the system and can therefore itself become time dependent. At weak coupling the array settles into a quiescent stationary state. Increasing coupling strength leads to a saddle node bifurcation, beyond which the quiescent state coexists with a stable limit cycle of nonlinear coherent oscillations. We explicitly determine the critical coupling constant for this transition

Memory-induced anomalous dynamics: emergence of diffusion, subdiffusion, and superdiffusion from a single random walk model

We present a random walk model that exhibits asymptotic subdiffusive, diffusive, and superdiffusive behavior in different parameter regimes. This appears to be the first instance of a single random walk model leading to all three forms of behavior by simply changing parameter values. Furthermore, the model offers the great advantage of analytic tractability. Our model is non-Markovian in that the next jump of the walker is (probabilistically) determined by the history of past jumps. It also has elements of intermittency in that one possibility at each step is that the walker does not move at all. This rich encompassing scenario arising from a single model provides useful insights into the source of different types of asymptotic behavior

Is subdiffusional transport slower than normal?

We consider anomalous non-Markovian transport of Brownian particles in viscoelastic fluid-like media with very large but finite macroscopic viscosity under the influence of a constant force field F. The viscoelastic properties of the medium are characterized by a power-law viscoelastic memory kernel which ultra slow decays in time on the time scale \tau of strong viscoelastic correlations. The subdiffusive transport regime emerges transiently for t<\tau. However, the transport becomes asymptotically normal for t>>\tau. It is shown that even though transiently the mean displacement and the variance both scale sublinearly, i.e. anomalously slow, in time, ~ F t^\alpha, ~ t^\alpha, 0<\alpha<1, the mean displacement at each instant of time is nevertheless always larger than one obtained for normal transport in a purely viscous medium with the same macroscopic viscosity obtained in the Markovian approximation. This can have profound implications for the subdiffusive transport in biological cells as the notion of "ultra-slowness" can be misleading in the context of anomalous diffusion-limited transport and reaction processes occurring on nano- and mesoscales

Nonequilibrium fluctuation induced escape from a metastable state

Based on a simple microscopic model where the bath is in a non-equilibrium state we study the escape from a metastable state in the over-damped limit. Making use of Fokker-Planck-Smoluchowski description we derive the time dependent escape rate in the non-stationary regime in closed analytical form which brings on to fore a strong non-exponential kinetic of the system mode.Comment: 4 pages, no figures, EPJ class file include

Phase Space Transport in Noisy Hamiltonian Systems

This paper analyses the effect of low amplitude friction and noise in accelerating phase space transport in time-independent Hamiltonian systems that exhibit global stochasticity. Numerical experiments reveal that even very weak non-Hamiltonian perturbations can dramatically increase the rate at which an ensemble of orbits penetrates obstructions like cantori or Arnold webs, thus accelerating the approach towards an invariant measure, i.e., a near-microcanonical population of the accessible phase space region. An investigation of first passage times through cantori leads to three conclusions, namely: (i) that, at least for white noise, the detailed form of the perturbation is unimportant, (ii) that the presence or absence of friction is largely irrelevant, and (iii) that, overall, the amplitude of the response to weak noise scales logarithmically in the amplitude of the noise.Comment: 13 pages, 3 Postscript figures, latex, no macors. Annals of the New York Academy of Sciences, in pres