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Pattern formation in nonextensive thermodynamics: selection criterion based on the Renyi entropy production
Olgierd Cybulski1, Daniel Matysiak, Volodymyr Babin
1Institute of Physical Chemistry, Polish Academy of Sciences, Warsaw. olgierd@ryba.ichf.edu.pl
The Journal of Chemical Physics
|May 25, 2005
Summary
This study analyzes Brownian particles that annihilate upon contact. The system evolves towards stationary states that minimize Renyi entropy production, even with dynamic interfaces.
Area of Science:
- Statistical physics
- Non-equilibrium systems
- Chemical kinetics
Background:
- Brownian motion describes random particle movement.
- Annihilation reactions occur when particles meet.
- Periodic boundary conditions simplify system analysis.
Purpose of the Study:
- To analyze a two-component Brownian particle system with annihilation.
- To identify stationary states and their relation to entropy production.
- To understand system evolution dynamics.
Main Methods:
- Simulation of Brownian particles in a cubic box.
- Analysis of particle annihilation and birth rates.
- Calculation of Renyi entropy production.
Main Results:
- Stationary states are characterized by an interface dividing particle types.
- These states correspond to Laplacian eigenfunctions.
- Renyi entropy production decreases monotonically during evolution.
Conclusions:
- The system self-organizes into distinct spatial domains.
- Minimization of Renyi entropy production drives the system's evolution.
- Interface dynamics are complex despite monotonic entropy decrease.