2,002 research outputs found
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
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 . While still alive, the creeper has a finite
mean frequency 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
-dependent optimal frequency that maximizes the
probability of eventual target detection. We work primarily in one-dimensional
() domains and examine the role of initial conditions and of finite domain
sizes. Numerical results in 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 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
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
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
Coagulation reaction in low dimensions: Revisiting subdiffusive A+A reactions in one dimension
We present a theory for the coagulation reaction A+A -> A for particles
moving subdiffusively in one dimension. Our theory is tested against numerical
simulations of the concentration of particles as a function of time
(``anomalous kinetics'') and of the interparticle distribution function as a
function of interparticle distance and time. We find that the theory captures
the correct behavior asymptotically and also at early times, and that it does
so whether the particles are nearly diffusive or very subdiffusive. We find
that, as in the normal diffusion problem, an interparticle gap responsible for
the anomalous kinetics develops and grows with time. This corrects an earlier
claim to the contrary on our part.Comment: The previous version was corrupted - some figures misplaced, some
strange words that did not belong. Otherwise identica
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