Related papers: Work distribution and path integrals in general me…
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…
We apply path integrals to study nonequilibrium work theorems in the context of Brownian dynamics, deriving in particular the equations of motion governing the most typical and most dominant trajectories. For the analytically soluble cases…
In the global framework of finding an axiomatic derivation of nonequilibrium Statistical Mechanics from fundamental principles, such as the maximum path entropy -- also known as Maximum Caliber principle -- , this work proposes an…
The study of the normalized sum of random variables and its asymptotic behaviour has been and continues to be a central chapter in probability and statistical mechanics. When those variables are independent the central limit theorem ensures…
We derive and solve a differential equation satisfied by the probability distribution of the work done on a single biomolecule in a mechanical unzipping experiment. The unzipping is described as a thermally activated escape process in an…
We present a general scheme to obtain work distribution in closed systems under continuous quantum histories of corresponding "power" operator. The scheme is tested by analytically calculating the quantum work distribution for a prototype…
We review and discuss the equations governing the distribution of work done on a system which is driven out of equilibrium by external manipulation, as well as those governing the entropy flow to a reservoir in a nonequilibrium system. We…
We study nonequilibrium work relations for a space-dependent field with stochastic dynamics (Model A). Jarzynski's equality is obtained through symmetries of the dynamical action in the path integral representation. We derive a set of exact…
We show that steady-state probabilities of a nonequilibrium Markovian system can be reconstructed from a weighted ensemble average of finite-time loop-erased paths. Each path $\Gamma$ is weighted by $e^{-S(\Gamma)}$, where $S(\Gamma)$ can…
Mean-field dynamo equations are addressed with the aid of the path-integral method. The evolution of magnetic field is treated as a three-dimensional Wiener random process, and the mean magnetic-field equations are obtained with the Wiener…
We use probabilistic methods to study properties of mean-field models, arising as large-scale limits of certain particle systems with mean-field interaction. The underlying particle system is such that $n$ particles move forward on the real…
We give a field-theoretic proof of the nonequilibrium work relations for a space dependent field with stochastic dynamics. The path integral representation and its symmetries allow us to derive Jarzynski's equality. In addition, we derive a…
Work statistics characterizes important features of a non-equilibrium thermodynamic process. But the calculation of the work statistics in an arbitrary non-equilibrium process is usually a cumbersome task. In this work, we study the work…
A path integral formalism for non-equilibrium systems is proposed based on a manifold of quasi-equilibrium densities. A generalized Boltzmann principle is used to weight manifold paths with the exponential of minus the information…
The Jarzynski equality, which relates equilibrium free-energy difference to an average of non-equilibrium work, plays a central role in modern non-equilibrium statistical thermodynamics. In this paper, we study a weaker consequence of this…
We derive a general information-theoretic equality for a system undergoing two projective measurements separated by a general temporal evolution. The equality implies the non-negativity of the mutual information between the measurement…
Although real-world complex systems typically interact through sparse and heterogeneous networks, analytic solutions of their dynamics are limited to models with all-to-all interactions. Here, we solve the dynamics of a broad range of…
Thermodynamics is a well developed tool to study systems in equilibrium but no such general framework is available for non-equilibrium processes. Only hope for a quantitative description is to fall back upon the equilibrium language as…
In this paper we introduce and discuss kinetic equations for the evolution of the probability distribution of the number of particles in a population subject to binary interactions. The microscopic binary law of interaction is assumed to be…
Recently there has been growing interest in extending the thermodynamic method from static configurations to dynamical trajectories. In this approach, ensembles of trajectories are treated in an analogous manner to ensembles of…