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11:03
An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Local kinetic interpretation of entropy production through reversed diffusion
A Porporato1, P R Kramer, M Cassiani
1Department of Civil and Environmental Engineering, Duke University, Durham, North Carolina, USA. amilcare@duke.edu
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 21, 2011
Summary
This study clarifies the physical meaning of time-reversed drift and noise in stochastic diffusion processes. It links diffusion kinematics to hydrodynamics and derives an equation for entropy production using the Girsanov theorem.
Area of Science:
- Statistical Physics
- Stochastic Processes
- Non-equilibrium Thermodynamics
Background:
- Stochastic diffusion processes are fundamental in physics.
- Understanding time reversal is crucial for non-equilibrium systems.
- Multiplicative noise introduces complexities in diffusion models.
Purpose of the Study:
- To revisit the time reversal of stochastic diffusion processes.
- To clarify the physical meaning of time-reversed drift and noise.
- To explore the connection between diffusion, hydrodynamics, and entropy production.
Main Methods:
- Analysis of time-reversed drift and noise prescriptions for multiplicative noise.
- Linking local diffusion kinematics to hydrodynamic descriptions.
- Application of the Girsanov theorem for reversed diffusion.
- Illustration using the Ornstein-Uhlenbeck process.
Main Results:
- Physical interpretation of time-reversed drift and noise.
- Connection between diffusion mechanics and hydrodynamic descriptions.
- Interpretation of the Pope-Ching formula and fluctuation-dissipation relation.
- Derivation of a stochastic differential equation for entropy production.
Conclusions:
- The study provides a deeper understanding of time reversal in stochastic diffusion.
- It establishes links between microscopic diffusion properties and macroscopic hydrodynamic descriptions.
- The findings offer new insights into entropy production in diffusion processes.
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