An Introduction To Stochastic Processes And Nonequilibrium Statistical Physics Pdf
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- Collective processes in non-equilibrium systems
- Stochastic Processes in Nonequilibrium Systems
- Elements of Nonequilibrium Statistical Mechanics
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Collective processes in non-equilibrium systems
Stochastic Processes in Nonequilibrium Systems
Opening Chapter 1. In the first chapter the reader can find the basic ingredients of elementary kinetic theory and of the mathematical approach to discrete and continuous stochastic processes. All that is necessary to establish a solid ground for nonequilibrium processes concerning the time evolution of physical systems subject to a statistical description. In fact, from the first sections we discuss problems where we deal with the time evolution of average quantities, like in the elementary random walk model of diffusion. We also illustrate the bases of transport phenomena that allow us to introduce the concept of transport coefficients, that will be reconsidered later in the framework of a more general theory see Chap. Then we focus on the theory of Brownian motion, as it was originally formulated by Albert Einstein and how this was later described in terms of the Langevin and of the Fokker-Planck equations, specialized to a Brownian particle.
Understanding the fluctuations by which phenomenological evolution equations with thermodynamic structure can be enhanced is the key to a general framework of nonequilibrium statistical mechanics. These fluctuations provide an idealized representation of microscopic details. We consider fluctuation-enhanced equations associated with Markov processes and elaborate the general recipes for evaluating dynamic material properties, which characterize force-flux constitutive laws, by statistical mechanics. Markov processes with continuous trajectories are conveniently characterized by stochastic differential equations and lead to Green—Kubo-type formulas for dynamic material properties. Markov processes with discontinuous jumps include transitions over energy barriers with the rates calculated by Kramers.
Elements of Nonequilibrium Statistical Mechanics
Reichl: A modern course in statisitical physics. Wiley-Interscience, New York Wilde and S.
Path integrals and perturbation theory for stochastic processes. We review and extend the formalism introduced by Peliti, that maps a Markov process to a path-integral representation. After developing the mapping, we apply it to some illustrative examples: the simple decay process, the birth-and-death process, and the Malthus-Verhulst process. In the fi rst two cases we show how to obtain the exact probability generating function using the path integral.