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Updated: Jun 21, 2026
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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Variational principle of counting statistics in master equations
1Institute for Solid State Physics, University of Tokyo, Kashiwanoha 5-1-5, Kashiwa-shi, Chiba 277-8581, Japan. ohkubo@issp.u-tokyo.ac.jp
Summary
This study presents a generalized path integral formulation for counting statistics in stochastic processes, applicable beyond mesoscopic systems. It establishes a valid saddle point method and derives a variational principle using system replicas and the Euler-Maclaurin formula.
Area of Science:
- Statistical Physics
- Stochastic Processes
- Quantum Field Theory
Background:
- Path integral formulations are established for counting statistics in mesoscopic systems.
- Previous methods relied on assumptions specific to mesoscopic scales.
Purpose of the Study:
- To generalize the path integral formulation for counting statistics beyond mesoscopic systems.
- To validate the saddle point method for path integrals in this broader context.
- To derive a variational principle for counting statistics.
Main Methods:
- Path integral formulation
- Saddle point method validation
- System replication technique
- Euler-Maclaurin formula application
Main Results:
- A generalized path integral formulation for counting statistics is derived, not limited to mesoscopic systems.
- The saddle point method is confirmed as a valid, non-approximate procedure.
- A variational principle for counting statistics is naturally derived.
Conclusions:
- The developed method offers a more universal approach to studying counting statistics.
- The findings provide a robust framework for analyzing stochastic processes.
- This work bridges discrete and continuous system properties via the Euler-Maclaurin formula.
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