Statistical mechanical theory for steady state systems. VII. Nonlinear theory.

Area of Science:

• Nonlinear Nonequilibrium Thermodynamics
• Statistical Mechanics
• Chemical Kinetics

Background:

• Second entropy theory traditionally applies to linear irreversible processes.
• Extending thermodynamic theories to nonlinear regimes is crucial for complex systems.
• Understanding systems with mixed parity (even/odd functions) is essential for broader applicability.

Purpose of the Study:

• To extend the second entropy theory into the nonlinear regime.
• To analyze systems composed of mixed parity functions of molecular velocities.
• To investigate the behavior of nonlinear transport matrices and their relation to established thermodynamic principles.

Main Methods:

• Development of a generalized second entropy theory for nonlinear systems.
• Derivation of the steady-state phase space probability density for mixed parity systems.
• Formulation and analysis of the nonlinear transport matrix.

Main Results:

• The nonlinear transport matrix yields an analog of the linear Onsager-Casimir reciprocal relations.
• The asymmetric part of the matrix contributes to flux and second entropy production.
• The first nonlinear correction to transport coefficients is explicitly expressed via a Green-Kubo type equilibrium time correlation function.

Conclusions:

• The extended theory provides a framework for nonlinear nonequilibrium thermodynamics in mixed parity systems.
• The findings offer new insights into the behavior of transport coefficients beyond linear approximations.
• The application to chemical kinetics demonstrates the practical relevance of the developed theory.