Symplectic Noise and the Classical Analog of the Lindblad GeneratorDoes the Regression Hypothesis also Fail in Classical Physics?

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Type Article
Original languageEnglish
Pages (from-to)1709-1720
JournalJournal of Statistical Physics
Issue number6
Early online date28 Jun 2015
Publication statusPublished - Sep 2015
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We introduce the concept of Poisson Brackets for classical noise and, in particular, for pairs of canonically conjugate Wiener processes (symplectic noise). Phase space diffusions driven by these processes are considered and the general form of a stochastic process preserving the full (system and noise) Poisson structure is obtained. Making the requirement that the classical stochastic model preserves the joint system and noise Poisson Brackets, we show that the model has actually much in common with quantum markovian models.


  • canonical, noise, symplectic, wiener