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Fluctuation theorems from non-equilibrium Onsager-Machlup theory for a Brownian particle in a time-dependent harmonic potential

100%
Deza R., Izús G., Wio H.
Open Physics
|
2009
|
vol. 7
|
issue 3
472-478
EN
We discuss the case of a Brownian particle which is harmonically bound and multiplicatively forced-namely bound by V(x,t)=1/2 a(t)x 2 where a(t)is externally controlled-as another instance that provides a generalization of Onsager-Machlup’s theory to non-equilibrium states, thus allowing establishment of several fluctuation theorems. In particular, we outline the derivation of a fluctuation theorem for work, through the calculation of the work probability distribution as a functional integral over stochastic trajectories.
2
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Lévy flights and Lévy-Schrödinger semigroups

84%
Garbaczewski P.
Open Physics
|
2010
|
vol. 8
|
issue 5
699-708
EN
We analyze two different confining mechanisms for Lévy flights in the presence of external potentials. One of them is due to a conservative force in the corresponding Langevin equation. Another is implemented by Lévy-Schrödinger semigroups which induce so-called topological Lévy processes (Lévy flights with locally modified jump rates in the master equation). Given a stationary probability function (pdf) associated with the Langevin-based fractional Fokker-Planck equation, we demonstrate that generically there exists a topological Lévy process with the same invariant pdf and in reverse.
3
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Generalized Fokker-Planck equation for a class of stochastic dynamical systems driven by additive Gaussian and Poissonian fractional white noises of order α

84%
Jumarie G.
Open Physics
|
2008
|
vol. 6
|
issue 3
737-753
EN
In a first stage, the paper deals with the derivation and the solution of the equation of the probability density function of a stochastic system driven simultaneously by a fractional Gaussian white noise and a fractional Poissonian white noise both of the same order. The key is the Taylor’s series of fractional order f(x + h) = E α(hαDx α)f(x) where E α() denotes the Mittag-Leffler function, and D x α is the so-called modified Riemann-Liouville fractional derivative which removes the effects of the non-zero initial value of the function under consideration. The corresponding fractional linear partial differential equation is solved by using a suitable extension of the Lagrange’s technique involving an auxiliary set of fractional differential equations. As an example, one considers a half-oscillator of fractional order driven by a fractional Poissonian noise.
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