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Stochastic Energetics for Non-Gaussian Stochastic Dynamics

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Statistical Mechanics for Athermal Fluctuation

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Abstract

Stochastic energetics is formulated for general non-Gaussian stochastic dynamics. Stochastic processes are first reformulated using smooth \(\delta \)-functions, and three kinds of products are introduced for smooth \(\delta \)-functions: the Itô, Stratonovich, and * products. By introducing the concept of the mixed products, where multiple products coexist, we show an extended ordinary chain rule valid for an arbitrary stochastic processes. This formulation is applied to stochastic energetics for general non-Gaussian dynamics. As demonstrations, we study energetics of the BGK kinetic model and the non-Gaussian–Langevin equation.

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  1. Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto, Japan

    Kiyoshi Kanazawa

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  1. Kiyoshi Kanazawa
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Correspondence to Kiyoshi Kanazawa .

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Kanazawa, K. (2017). Stochastic Energetics for Non-Gaussian Stochastic Dynamics. In: Statistical Mechanics for Athermal Fluctuation. Springer Theses. Springer, Singapore. https://doi.org/10.1007/978-981-10-6332-9_9

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  • DOI: https://doi.org/10.1007/978-981-10-6332-9_9

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  • Print ISBN: 978-981-10-6330-5

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