Non quantum uncertainty relations of stochastic dynamics

Details Non quantum uncertainty relations of stochastic dynamics Non quantum uncertainty relations of stochastic dynamics

2004-12-14

arxiv.org/abs/cond-mat/0412360v2

Chaos, Solitons and Fractals 26 (2005) 1045

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

First we describe briefly an information-action method for the study of stochastic dynamics of hamiltonian systems perturbed by thermal noise and chaotic instability. It is shown that, for the ensemble of possible paths between two configuration points, the action principle acquires a statistical form $<\delta A>=0$. The main objective of this paper is to prove that, via this information-action description, some quantum like uncertainty relations such as $<\Delta A>\geq\frac{1}{\sqrt{2}\eta}$ for action, $<\Delta x><\Delta P>\geq\frac{1}{\eta}$ for position and momentum, and $<\Delta H><\Delta t>\geq\frac{1}{\sqrt{2}\eta}$ for hamiltonian and time, can arise for stochastic dynamics of classical hamiltonian systems. A corresponding commutation relation can also be found. These relations describe, through action or its conjugate variables, the fluctuation of stochastic dynamics due to random perturbation characterized by the parameter $\eta$.

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