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

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

Absence of jump discontinuity in the magnetization in quasi-one-dimensional random-field Ising models

We consider the zero-temperature random-field Ising model in the presence of an external field, on ladders and in one dimension with finite range interactions, for unbounded continuous distributions of random fields, and show that there is no jump discontinuity in the magnetizations for any quasi-one dimensional model. We show that the evolution of the system at an external field can be described by a stochastic matrix and the magnetization can be obtained using the eigenvector of the matrix corresponding to the eigenvalue one, which is continuous and differentiable function of the external field.Comment: 4 pages, 5 ps figures. Minor correction