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Study of entropy-diffusion relation in deterministic Hamiltonian systems through microscopic analysis
Subhajit Acharya1, Biman Bagchi1
1Solid State and Structural Chemistry Unit, Indian Institute of Science, Bengaluru, India.
The Journal of Chemical Physics
|November 14, 2020
Summary
This study investigates the quantitative relationship between entropy and diffusion in deterministic systems. Researchers found a crossover in this relation, suggesting a breakdown of existing scaling laws and proposing a modified model.
Area of Science:
- Statistical Mechanics
- Non-equilibrium Thermodynamics
- Computational Physics
Background:
- The relationship between entropy and diffusion is theoretically established but lacks quantitative validation.
- Existing models, like Rosenfeld-like exponential scaling, may not fully capture complex system dynamics.
Purpose of the Study:
- To quantitatively explore the entropy-diffusion relation in deterministic systems.
- To investigate potential breakdowns in established scaling laws.
- To propose a modified relation accounting for correlated motions.
Main Methods:
- Computer simulations to estimate self-diffusion coefficients.
- Quadrature methods using Boltzmann's formula for entropy estimation.
- Analysis of three deterministic model systems: periodic potential, Lorentz gas, and apertured boxes.
Main Results:
- Observed a crossover in the diffusion-entropy relation in specific regions.
- Attributed this crossover to the emergence of correlated particle returns.
- Demonstrated a potential breakdown of Rosenfeld-like exponential scaling.
Conclusions:
- The study provides a quantitative analysis of the entropy-diffusion link in deterministic systems.
- Correlated returns introduce complexities that necessitate modifications to existing theoretical frameworks.
- Dynamical entropy, derived from Lyapunov exponents, offers insights into deterministic system behavior.
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