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Stochastic processes: Time evolution, symmetries and linear response
Peter Hänggi,Harry Thomas +1 more
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This article is published in Physics Reports.The article was published on 1982-08-01. It has received 560 citations till now. The article focuses on the topics: Continuous-time stochastic process & Stochastic calculus.read more
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The random walk's guide to anomalous diffusion: a fractional dynamics approach
Ralf Metzler,Joseph Klafter +1 more
TL;DR: Fractional kinetic equations of the diffusion, diffusion-advection, and Fokker-Planck type are presented as a useful approach for the description of transport dynamics in complex systems which are governed by anomalous diffusion and non-exponential relaxation patterns.
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Reaction-rate theory: fifty years after Kramers
TL;DR: In this paper, the authors report, extend, and interpret much of our current understanding relating to theories of noise-activated escape, for which many of the notable contributions are originating from the communities both of physics and of physical chemistry.
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Stochastic thermodynamics, fluctuation theorems and molecular machines
TL;DR: Efficiency and, in particular, efficiency at maximum power can be discussed systematically beyond the linear response regime for two classes of molecular machines, isothermal ones such as molecular motors, and heat engines such as thermoelectric devices, using a common framework based on a cycle decomposition of entropy production.
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Brownian motors: noisy transport far from equilibrium
TL;DR: In this paper, the main emphasis is put on directed transport in so-called Brownian motors (ratchets), i.e. a dissipative dynamics in the presence of thermal noise and some prototypical perturbation that drives the system out of equilibrium without introducing a priori an obvious bias into one or the other direction of motion.
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Shot noise in mesoscopic conductors
TL;DR: Theoretical and experimental work concerned with dynamic fluctuations has developed into a very active and fascinating subfield of mesoscopic physics as discussed by the authors, which can be used to obtain information on a system which is not available through conductance measurements.
References
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Book
Probability, random variables and stochastic processes
TL;DR: This chapter discusses the concept of a Random Variable, the meaning of Probability, and the axioms of probability in terms of Markov Chains and Queueing Theory.
Book
Probability, random variables, and stochastic processes
TL;DR: In this paper, the meaning of probability and random variables are discussed, as well as the axioms of probability, and the concept of a random variable and repeated trials are discussed.
Book
Phase Transitions and Critical Phenomena
TL;DR: The field of phase transitions and critical phenomena continues to be active in research, producing a steady stream of interesting and fruitful results as discussed by the authors, and the major aim of this serial is to provide review articles that can serve as standard references for research workers in the field.