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Statistical formulation of the Onsager-Machlup variational principle
Kento Yasuda1, Kenta Ishimoto1, Shigeyuki Komura2,3,4
1Research Institute for Mathematical Sciences, <a href="https://ror.org/02kpeqv85">Kyoto University</a>, Kyoto 606-8502, Japan.
Physical Review. E
|November 20, 2024
Summary
This study reformulates the Onsager-Machlup variational principle (OMVP) to incorporate thermal fluctuations in soft and active matter. The new method successfully calculates diffusion constants for Brownian particles in viscous fluids and shear flow.
Area of Science:
- Soft Matter Physics
- Statistical Mechanics
- Non-Equilibrium Systems
Background:
- Onsager's variational principle offers a systematic method for deriving dynamical equations in soft and active matter.
- The Onsager-Machlup variational principle (OMVP) is a time-global principle that can be reformulated for enhanced applications.
Purpose of the Study:
- To propose a novel method for incorporating thermal fluctuations by reformulating the OMVP.
- To demonstrate the utility of this statistical formulation in calculating physical properties of matter.
Main Methods:
- Reformulation of the Onsager-Machlup variational principle (OMVP).
- Maximization of the modified Onsager-Machlup integral for surrounding fluids.
- Application to Brownian particles in viscous fluids and steady shear flow.
Main Results:
- Successfully obtained the diffusion constant for a Brownian particle in a viscous fluid.
- Applied the formulation to a Brownian particle in a steady shear flow, a non-equilibrium system.
- Demonstrated the effectiveness of the statistical formulation of OMVP.
Conclusions:
- The reformulated OMVP provides a powerful tool for incorporating thermal fluctuations.
- The method is applicable to both equilibrium and non-equilibrium systems.
- Potential extensions to internally driven active systems are discussed.
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