380 research outputs found

### The distribution function of entropy flow in stochastic systems

We obtain a simple direct derivation of the differential equation governing
the entropy flow probability distribution function of a stochastic system first
obtained by Lebowitz and Spohn. Its solution agrees well with the experimental
results of Tietz et al [2006 {\it Phys. Rev. Lett.} {\bf 97} 050602]. A
trajectory-sampling algorithm allowing to evaluate the entropy flow
distribution function is introduced and discussed. This algorithm turns out to
be effective at finite times and in the case of time-dependent transition
rates, and is successfully applied to an asymmetric simple exclusion process

### Evaluation of free energy landscapes from manipulation experiments

A fluctuation relation, which is an extended form of the Jarzynski equality,
is introduced and discussed. We show how to apply this relation in order to
evaluate the free energy landscape of simple systems. These systems are
manipulated by varying the external field coupled with a systems' internal
characteristic variable. Two different manipulation protocols are here
considered: in the first case the external field is a linear function of time,
in the second case it is a periodic function of time. While for simple mean
field systems both the linear protocol and the oscillatory protocol provide a
reliable estimate of the free energy landscape, for a simple model
ofhomopolymer the oscillatory protocol turns out to be not reliable for this
purpose. We then discuss the possibility of application of the method here
presented to evaluate the free energy landscape of real systems, and the
practical limitations that one can face in the realization of an experimental
set-up

### Work probability distribution in systems driven out of equilibrium

We derive the differential equation describing the time evolution of the work
probability distribution function of a stochastic system which is driven out of
equilibrium by the manipulation of a parameter. We consider both systems
described by their microscopic state or by a collective variable which
identifies a quasiequilibrium state. We show that the work probability
distribution can be represented by a path integral, which is dominated by
``classical'' paths in the large system size limit. We compare these results
with simulated manipulation of mean-field systems. We discuss the range of
applicability of the Jarzynski equality for evaluating the system free energy
using these out-of-equilibrium manipulations. Large fluctuations in the work
and the shape of the work distribution tails are also discussed

### Efficiency of molecular machines with continuous phase space

We consider a molecular machine described as a Brownian particle diffusing in
a tilted periodic potential. We evaluate the absorbed and released power of the
machine as a function of the applied molecular and chemical forces, by using
the fact that the times for completing a cycle in the forward and the backward
direction have the same distribution, and that the ratio of the corresponding
splitting probabilities can be simply expressed as a function of the applied
force. We explicitly evaluate the efficiency at maximum power for a simple
sawtooth potential. We also obtain the efficiency at maximum power for a broad
class of 2-D models of a Brownian machine and find that loosely coupled
machines operate with a smaller efficiency at maximum power than their strongly
coupled counterparts.Comment: To appear in EP

### Proportion of Unaffected Sites in a Reaction-Diffusion Process

We consider the probability $P(t)$ that a given site remains unvisited by any
of a set of random walkers in $d$ dimensions undergoing the reaction $A+A\to0$
when they meet. We find that asymptotically $P(t)\sim t^{-\theta}$ with a
universal exponent \theta=\ffrac12-O(\epsilon) for $d=2-\epsilon$, while, for
$d>2$, $\theta$ is non-universal and depends on the reaction rate. The
analysis, which uses field-theoretic renormalisation group methods, is also
applied to the reaction $kA\to0$ with $k>2$. In this case, a stretched
exponential behaviour is found for all $d\geq1$, except in the case $k=3$,
$d=1$, where P(t)\sim {\rm e}^{-\const (\ln t)^{3/2}}.Comment: 10 pages, (revised version with abstract included) OUTP-94-35

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