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Related Experiment Video

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Image-based Lagrangian Particle Tracking in Bed-load Experiments

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Published on: July 20, 2017

Marcus canonical integral for non-Gaussian processes and its computation: pathwise simulation and tau-leaping

Tiejun Li¹, Bin Min, Zhiming Wang

¹Laboratory of Mathematics and Applied Mathematics and School of Mathematical Sciences, Peking University, Beijing 100871, People's Republic of China. tieli@pku.edu.cn

The Journal of Chemical Physics

|March 22, 2013

Summary

This study introduces the Marcus integral for non-Gaussian processes, crucial for stochastic energetics. It details computation methods and thermodynamic quantity calculations, enhancing physicist understanding.

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Last Updated: May 13, 2026

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Published on: July 20, 2017

Area of Science:

Physics
Physical Chemistry
Stochastic Processes

Background:

The Newton-Leibnitz chain rule in stochastic energetics relies on specific stochastic integrals.
The Marcus canonical integral satisfies this property, acting as a Wong-Zakai smoothing limit for non-Gaussian processes.
This concept is not widely recognized among physicists.

Purpose of the Study:

To discuss the Marcus integral for non-Gaussian processes within stochastic energetics.
To provide a comprehensive introduction to the Marcus integral and its definitions.
To present computational methods and their application to thermodynamic quantities.

Main Methods:

Comparison of three equivalent definitions of the Marcus integral.
Introduction of an exact pathwise simulation algorithm with error analysis.
Development and proposal of the tau-leaping algorithm for advancing processes.
Numerical experiments and efficiency analysis.

Main Results:

The Marcus integral is essential for stochastic energetics with non-Gaussian processes.
Pathwise simulation and tau-leaping algorithms enable computation of thermodynamic quantities.
The Marcus mapping reveals information critical for determining thermodynamic quantities.
The tau-leaping algorithm shows promising efficiency.

Conclusions:

The Marcus integral is a vital tool for stochastic energetics, particularly for non-Gaussian processes.
Proposed algorithms facilitate the computation of thermodynamic quantities, bridging theory and simulation.
Further research into the Marcus mapping can deepen the understanding of stochastic thermodynamics.