Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2012-03-29
Physics
Condensed Matter
Statistical Mechanics
18 pages, 1 figure
Scientific paper
Recently, a novel framework to handle stochastic processes emerges from a series of studies in biology, showing situations beyond "Ito vs. Stratonovich". Its internal consistency can be demonstrated via the zero mass limit of a generalized Klein-Kramers equation. Moreover, the connection to other integrations becomes evident: The obtained Fokker-Planck equation defines a new type of stochastic calculus that in general differs from the $\alpha$-type interpretation. A unique advantage of this new approach is a natural correspondence between stochastic and deterministic dynamics, which is useful or may even be essential in practice. The core of the framework is a transformation from a usual Langevin equation to a form that contains a potential function with two additional dynamical matrices, which reveals an underlying symplectic structure. The framework has a direct physical meaning and a straightforward experimental realization. Indeed, a recent experiment offers a first empirical validation of such new stochastic integration.
Ao Ping
Yuan Ruoshi
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