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This book provides an introductory albeit solid presentation of
path integration techniques as applied to the field of stochastic
processes. The subject began with the work of Wiener during the
1920's, corresponding to a sum over random trajectories,
anticipating by two decades Feynman's famous work on the path
integral representation of quantum mechanics. However, the true
trigger for the application of these techniques within
nonequilibrium statistical mechanics and stochastic processes was
the work of Onsager and Machlup in the early 1950's. The last
quarter of the 20th century has witnessed a growing interest in
this technique and its application in several branches of research,
even outside physics (for instance, in economy).The aim of this
book is to offer a brief but complete presentation of the path
integral approach to stochastic processes. It could be used as an
advanced textbook for graduate students and even ambitious
undergraduates in physics. It describes how to apply these
techniques for both Markov and non-Markov processes. The path
expansion (or semiclassical approximation) is discussed and adapted
to the stochastic context. Also, some examples of nonlinear
transformations and some applications are discussed, as well as
examples of rather unusual applications. An extensive bibliography
is included. The book is detailed enough to capture the interest of
the curious reader, and complete enough to provide a solid
background to explore the research literature and start exploiting
the learned material in real situations. remove
This book aims to provide a compact and unified introduction to the
most important aspects in the physics of non-equilibrium systems.
It first introduces stochastic processes and some modern tools and
concepts that have proved their usefulness to deal with
non-equilibrium systems from a purely probabilistic angle. The aim
is to show the important role played by fluctuations in
far-from-equilibrium situations, where noise can promote order and
organization, switching among non-equilibrium states, etc. The
second part adopts a more historical perspective, retracing the
first steps taken from the purely thermodynamic as well as from the
kinetic points of view to depart (albeit slightly) from
equilibrium. The third part revisits the path outlined in the first
one, but now undertakes the mesoscopic description of extended
systems, where new phenomena (patterns, long-range correlations,
scaling far from equilibrium, etc.) are observed.This book is a
revised and extended version of an earlier edition published in
1994. It includes topics of current research interest in
far-from-equilibrium situations like noise-induced phenomena and
free energy-like functionals, surface growth and roughening, etc.
It can be used as an advanced textbook by graduate students in
physics. It also covers topics of current interest in other
disciplines and interdisciplinary approaches in engineering,
biophysics, and economics, among others. The level of detail in the
book is enough to capture the interest of the reader and facilitate
the path to more learning by exploring the modern research
literature provided. At the same time, the book is also complete
enough to be self-contained for those readers who just need an
overview of the subject.
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