153 research outputs found
Statistical properties of single-file diffusion front
Statistical properties of the front of a semi-infinite system of single-file
diffusion (one dimensional system where particles cannot pass each other, but
in-between collisions each one independently follow diffusive motion) are
investigated. Exact as well as asymptotic results are provided for the
probability density function of (a) the front-position, (b) the maximum of the
front-positions, and (c) the first-passage time to a given position. The
asymptotic laws for the front-position and the maximum front-position are found
to be governed by the Fisher-Tippett-Gumbel extreme value statistics. The
asymptotic properties of the first-passage time is dominated by a
stretched-exponential tail in the distribution. The farness of the front with
the rest of the system is investigated by considering (i) the gap from the
front to the closest particle, and (ii) the density profile with respect to the
front-position, and analytical results are provided for late time behaviors.Comment: 4 revtex page
Work fluctuations for a harmonic oscillator driven by an external random force
The fluctuations of the work done by an external Gaussian random force on a
harmonic oscillator that is also in contact with a thermal bath is studied. We
have obtained the exact large deviation function as well as the complete
asymptotic forms of the probability density function. The distribution of the
work done are found to be non-Gaussian. The steady state fluctuation theorem
holds only if the ratio of the variances, of the external random forcing and
the thermal noise respectively, is less than 1/3. On the other hand, the
transient fluctuation theorem holds (asymptotically) for all the values of that
ratio. The theoretical asymptotic forms of the probability density function are
in very good agreement with the numerics as well as with an experiment.Comment: 6 pages, 4 figure
Record Statistics of Continuous Time Random Walk
The statistics of records for a time series generated by a continuous time
random walk is studied, and found to be independent of the details of the jump
length distribution, as long as the latter is continuous and symmetric.
However, the statistics depend crucially on the nature of the waiting time
distribution. The probability of finding M records within a given time duration
t, for large t, has a scaling form, and the exact scaling function is obtained
in terms of the one-sided Levy stable law. The mean of the ages of the records,
defined as , differs from t/. The asymptotic behaviour of the shortest
and the longest ages of the records are also studied.Comment: 5 pages, 3 figures; EPL published versio
Fluctuation theorem for entropy production of a partial system in the weak coupling limit
Small systems in contact with a heat bath evolve by stochastic dynamics. Here
we show that, when one such small system is weakly coupled to another one, it
is possible to infer the presence of such weak coupling by observing the
violation of the steady state fluctuation theorem for the partial entropy
production of the observed system. We give a general mechanism due to which the
violation of the fluctuation theorem can be significant, even for weak
coupling. We analytically demonstrate on a realistic model system that this
mechanism can be realized by applying an external random force to the system.
In other words, we find a new fluctuation theorem for the entropy production of
a partial system, in the limit of weak coupling.Comment: 7 pages, 3 figure
Driven inelastic Maxwell gases
We consider the inelastic Maxwell model, which consists of a collection of
particles that are characterized by only their velocities, and evolving through
binary collisions and external driving. At any instant, a particle is equally
likely to collide with any of the remaining particles. The system evolves in
continuous time with mutual collisions and driving taken to be point processes
with rates and respectively. The mutual collisions
conserve momentum and are inelastic, with a coefficient of restitution . The
velocity change of a particle with velocity , due to driving, is taken to be
, mimicking the collision with a vibrating wall,
where the coefficient of restitution of the particle with the "wall" and
is Gaussian white noise. The Ornstein-Uhlenbeck driving mechanism given
by is found to be a special case of the driving
modeled as a point process. Using both the continuum and discrete versions we
show that while the equations for the one-particle and the two-particle
velocity distribution functions do not close, the joint evolution equations of
the variance and the two-particle velocity correlation functions close. With
the exact formula for the variance we find that, for , the system
goes to a steady state. On the other hand, for , the system does not
have a steady state. Similarly, the system goes to a steady state for the
Ornstein-Uhlenbeck driving with , whereas for the purely
diffusive driving (), the system does not have a steady state.Comment: 9 pages, 4 figure
Heat and work fluctuations for a harmonic oscillator
The formalism of Kundu et al. [J. Stat. Mech. (2011) P03007], for computing
the large deviations of heat flow in harmonic systems, is applied to the case
of single Brownian particle in a harmonic trap and coupled to two heat baths at
different temperatures. The large-t form of the moment generating function
~ g(s) exp[t m(s)], of the total heat flow Q from one of the baths
to the particle in a given time interval t, is studied and exact explicit
expressions are obtained for both m(s) and g(s). For a special case of the
single particle problem that corresponds to the work done by an external
stochastic force on a harmonic oscillator coupled to a thermal bath, the
large-t form of the moment generating function is analyzed to obtain the exact
large deviation function as well as the complete asymptotic forms of the
probability density function of the work.Comment: 11 pages, 6 figure
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