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Non-quantum uncertainty relations of stochastic dynamics

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  • Wang, Qiuping A.

Abstract

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 〈δA〉=0. The main objective of this paper is to prove that, via this information-action description, some quantum like uncertainty relations such as 〈ΔA〉⩾12η for action, 〈Δx〉〈ΔP〉⩾1η for position and momentum, and 〈ΔH〉〈Δt〉⩾12η 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 η.

Suggested Citation

  • Wang, Qiuping A., 2005. "Non-quantum uncertainty relations of stochastic dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 26(4), pages 1045-1052.
    • Handle: RePEc:eee:chsofr:v:26:y:2005:i:4:p:1045-1052
    DOI: 10.1016/j.chaos.2005.03.012
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    1. Kaniadakis, G., 2002. "Statistical origin of quantum mechanics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 307(1), pages 172-184.
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    Cited by:

    1. Lucia, Umberto, 2013. "Thermodynamic paths and stochastic order in open systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(18), pages 3912-3919.
    2. Lin, T.L. & Wang, R. & Bi, W.P. & El Kaabouchi, A. & Pujos, C. & Calvayrac, F. & Wang, Q.A., 2013. "Path probability distribution of stochastic motion of non dissipative systems: a classical analog of Feynman factor of path integral," Chaos, Solitons & Fractals, Elsevier, vol. 57(C), pages 129-136.
    3. Wang, Q.A. & Bangoup, S. & Dzangue, F. & Jeatsa, A. & Tsobnang, F. & Le Méhauté, A., 2009. "Reformulation of a stochastic action principle for irregular dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2550-2556.
    4. Lucia, Umberto, 2013. "Stationary open systems: A brief review on contemporary theories on irreversibility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(5), pages 1051-1062.
    5. Lucia, Umberto, 2014. "Entropy generation and the Fokker–Planck equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 393(C), pages 256-260.
    6. Umberto Lucia, 2014. "The Gouy-Stodola Theorem in Bioenergetic Analysis of Living Systems (Irreversibility in Bioenergetics of Living Systems)," Energies, MDPI, vol. 7(9), pages 1-23, September.

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