Book ChapterDOI
Fokker-Planck Equation
Hannes Risken
- pp 63-95
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TLDR
In this paper, an equation for the distribution function describing Brownian motion was first derived by Fokker [11] and Planck [12] and it is shown that expectation values for nonlinear Langevin equations (367, 110) are much more difficult to obtain.Abstract:
As shown in Sects 31, 2 we can immediately obtain expectation values for processes described by the linear Langevin equations (31, 31) For nonlinear Langevin equations (367, 110) expectation values are much more difficult to obtain, so here we first try to derive an equation for the distribution function As mentioned already in the introduction, a differential equation for the distribution function describing Brownian motion was first derived by Fokker [11] and Planck [12]: many review articles and books on the Fokker-Planck equation now exist [15 – 15]read more
Citations
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Journal ArticleDOI
Inertial effects on the Brownian gyrator.
TL;DR: In this paper, the authors investigated how inertia can change the dynamics and energy of the Brownian gyrator and showed that the Langevin dynamics description of the gyrators is intrinsically different from that with Brownian dynamics.
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The Paradox of Information Access: On Modeling Social-Media-Induced Polarization.
TL;DR: A stochastic model of drift in human beliefs shows that today's sheer volume of accessible information, combined with consumers' confirmation bias and natural preference to more outlying content, necessarily lead to increased polarization, which explains the paradox of growing ideological fragmentation in the age of increased sharing.
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Predictive Collective Variable Discovery with Deep Bayesian Models
TL;DR: In this paper, the discovery of CVs is formulated as a Bayesian inference problem and considered the CVs as hidden generators of the full-atomistic trajectory of complex atomistic systems.
Journal ArticleDOI
Critical behaviour of the stochastic Wilson-Cowan model.
TL;DR: In this article, the existence of a bona fide critical point, where a second-order-like phase transition occurs, characterized by scale-free avalanche dynamics, scaling with the system size and a diverging relaxation time-scale.
Journal ArticleDOI
On the Master-Equation Approach to Kinetic Theory: Linear and Nonlinear Fokker-Planck Equations
TL;DR: In this paper, the relationship between the Fokker-Plank equations and the Kolmogorov (a.k.a. master) equations of certain N-body diffusion processes is discussed.
References
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Journal ArticleDOI
Fluctuations and Irreversible Processes
Lars Onsager,S. Machlup +1 more
TL;DR: In this paper, the probability of a given succession of (nonequilibrium) states of a spontaneously fluctuating thermodynamic system is calculated, on the assumption that the macroscopic variables defining a state are Gaussian random variables whose average behavior is given by the laws governing irreversible processes.
Journal ArticleDOI
The Radiation Theories of Tomonaga, Schwinger, and Feynman
TL;DR: In this article, a unified development of the subject of quantum electrodynamics is outlined, embodying the main features both of the Tomonaga-Schwinger and of the Feynman radiation theory.
Journal ArticleDOI
Covariant formulation of non-equilibrium statistical thermodynamics
TL;DR: In this paper, the diffusion matrix of the Fokker Planck equation is used as a contravariant metric tensor in phase space, and the covariance of the Langevin-equations and the fokker equation is demonstrated.
Journal ArticleDOI
Approximation of the Linear Boltzmann Equation by the Fokker-Planck Equation
TL;DR: In this article, the first two terms of the Kramers-Moyal expansion of the Fokker-Planck equation were used to approximate the linear Boltzmann integral operator.