Path integral formulations

Feynman path integrals, esp for stochastic processes



Applications of the famous Feynman-style path integral for quantum systems to non-quantum systems. Nothing to say here yet. Keywords: Onsager-Machlup.

References

Beretta, Gian Paolo. 2020. “The Fourth Law of Thermodynamics: Steepest Entropy Ascent.” Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 378 (2170): 20190168. https://doi.org/10.1098/rsta.2019.0168.
Borgerding, Mark, and Philip Schniter. 2016. “Onsager-Corrected Deep Networks for Sparse Linear Inverse Problems.” December 4, 2016. http://arxiv.org/abs/1612.01183.
Buzinov, M. S. 2017. “Feynman Formulas for Semigroups Generated by an Iterated Laplace Operator.” Russian Journal of Mathematical Physics 24 (2): 272–77. https://doi.org/10.1134/S1061920817020133.
Hasegawa, Yoshihiko, and Tan Van Vu. 2019. “Uncertainty Relations in Stochastic Processes: An Information Inequality Approach.” Physical Review E 99 (6): 062126. https://doi.org/10.1103/PhysRevE.99.062126.
Li, Yang, Jinqiao Duan, and Xianbin Liu. 2021. “Machine Learning Framework for Computing the Most Probable Paths of Stochastic Dynamical Systems.” Physical Review E 103 (1): 012124. https://doi.org/10.1103/PhysRevE.103.012124.
Onsager, L., and S. Machlup. 1953. “Fluctuations and Irreversible Processes.” Physical Review 91 (6): 1505–12. https://doi.org/10.1103/PhysRev.91.1505.
Sethna, James P. 2006. Statistical Mechanics: Entropy, Order Parameters, and Complexity. Oxford University Press, USA.
Westbroek, Marise J. E., Peter R. King, Dimitri D. Vvedensky, and Stephan Durr. 2018. “User’s Guide to Monte Carlo Methods for Evaluating Path Integrals.” American Journal of Physics 86 (4): 293–304. https://doi.org/10.1119/1.5024926.
Wio, Horacio S. 2013. Path Integrals for Stochastic Processes: An Introduction. WORLD SCIENTIFIC. https://doi.org/10.1142/8695.
Zinn-Justin, Jean. 2009. “Path Integral.” Scholarpedia 4 (2): 8674. https://doi.org/10.4249/scholarpedia.8674.

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