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We derive a simple closed analytical expression for the total entropy production along a single stochastic trajectory of a Brownian particle diffusing on a periodic potential under an external constant force. By numerical simulations we…
For Brownian motion of a single particle subject to a tilted periodic potential on a ring, we propose a formula for experimentally determining the cumulant generating function of time-averaged current without measurements of current…
We introduce innovative inference procedures for analyzing time series data. Our methodology enables density approximation and composite hypothesis testing based on Whittle's estimator, a widely applied M-estimator in the frequency domain.…
There is an abundance of useful fluctuation identities for one-sided L\'evy processes observed up to an independent exponentially distributed time horizon. We show that all the fundamental formulas generalize to time horizons having matrix…
We propose a simpler derivation of the probability density function of Feller Diffusion using the Fourier Transform and solving the resulting equation via the Method of Characteristics. We also discuss simulation algorithms and confirm key…
We derive the distribution function of work performed by a harmonic force acting on a uniformly dragged Brownian particle subjected to a rotational torque. Following the Onsager and Machlup's functional integral approach, we obtain the…
We introduce the notion of a Young generating function for a probability measure on integer partitions. We use this object to characterize probability distributions over integer partitions satisfying a law of large numbers and those that…
This paper describes a technique for analyzing the stochastic structure of the vectorial capacity using moment--generating functions. In such formulation, for an infectious disease transmitted by a vector, we obtain the generating function…
We study experimentally the thermal fluctuations of energy input and dissipation in a harmonic oscillator driven out of equilibrium, and search for Fluctuation Relations. We study transient evolution from the equilibrium state, together…
Projective measurements of a single two-level quantum mechanical system (a qubit) evolving under a time-independent Hamiltonian produce a probability distribution that is periodic in the evolution time. The period of this distribution is an…
Analytical work probability distributions for open classical systems are scarce; they can only be calculated in a few examples. In this work, I present a new method to derive such quantities for weakly driven processes in the overdamped…
A Gaussian fluctuation formula is proved for linear statistics of complex random matrices in the case that the statistic is rotationally invariant. For a general linear statistic without this symmetry, Coulomb gas theory is used to predict…
We consider a driven Brownian particle, subject to both conservative and non-conservative applied forces, whose probability evolves according to the Kramers equation. We derive a general fluctuation relation, expressing the ratio of the…
In this paper we review some general properties of probability distributions which exibit a singular behavior. After introducing the matter with several examples based on various models of statistical mechanics, we discuss, with the help of…
The concept of time emerges as an ordering structure in a classical statistical ensemble. Probability distributions $p_\tau(t)$ at a given time $t$ obtain by integrating out the past and future. We discuss all-time probability distributions…
We consider the relation between the microscopic and effective descriptions of the unfolding experiment on a model polypeptide. We evaluate the probability distribution function of the performed work by Monte Carlo simulations and compare…
We prove several general formulas for the distributions of various permutation statistics over any set of permutations whose quasisymmetric generating function is a symmetric function. Our formulas involve certain kinds of plethystic…
We study discrete probabilistic programs with potentially unbounded looping behaviors over an infinite state space. We present, to the best of our knowledge, the first decidability result for the problem of determining whether such a…
We consider the problem of function estimation in the case where the data distribution may shift between training and test time, and additional information about it may be available at test time. This relates to popular scenarios such as…
Fractional calculus allows one to generalize the linear, one-dimensional, diffusion equation by replacing either the first time derivative or the second space derivative by a derivative of fractional order. The fundamental solutions of…