Entropy production of diffusion in spatially periodic deterministic systems

Area of Science:

• Statistical Mechanics
• Thermodynamics
• Dynamical Systems

Background:

• Irreversible thermodynamics provides a framework for understanding entropy production in non-equilibrium systems.
• Diffusive processes in complex systems, such as Lorentz gases and interacting particle systems, are crucial for understanding macroscopic behavior.
• Chaotic dynamical systems offer models for studying fundamental properties of transport and entropy generation.

Purpose of the Study:

• To derive ab initio expressions for the rate of entropy production in specific classes of diffusive processes.
• To extend existing methods for calculating entropy production to higher-dimensional, continuous-time dynamical systems.
• To connect entropy production to fractal properties of microscopic hydrodynamic modes.

Main Methods:

• Derivation using irreversible thermodynamics principles.
• Application to Lorentz gases with noninteracting particles on a lattice.
• Analysis of periodic systems with N interacting particles and a tracer.
• Extension of methods from chaotic multi-baker map models.
• Analysis of deterministic, hyperbolic dynamics with positive Lyapunov exponents.

Main Results:

• An ab initio expression for the rate of entropy production was derived for the studied diffusive systems.
• The derivation was successfully extended from 2D chaotic models to higher-dimensional, continuous-time systems.
• The rate of entropy production is expressed in terms of hydrodynamic measures.
• These measures are linked to the fractal properties of the slowest decaying microscopic hydrodynamic modes.

Conclusions:

• The study provides a theoretical framework for calculating entropy production in complex diffusive systems.
• The findings highlight the role of fractal properties of hydrodynamic modes in determining entropy production rates.
• This work advances the understanding of non-equilibrium statistical mechanics and transport phenomena.