Nonlinear closure relations theory for transport processes in nonequilibrium systems

Area of Science:

• Non-equilibrium thermodynamics
• Plasma physics
• Chemical kinetics

Background:

• A macroscopic theory for closure relations, thermodynamic field theory (TFT), was proposed for systems outside Onsager's region.
• Existing TFT formulations have restrictions, including closed-form solutions for transport coefficients and the general covariance principle.

Purpose of the Study:

• To determine nonlinear flux-force relations respecting thermodynamic theorems for systems far from equilibrium.
• To propose a modified TFT formulation removing restrictions on transport coefficients and employing the De Donder-Prigogine thermodynamic covariance principle (TCP).

Main Methods:

• Developed an entropy-covariant formalism based on TCP.
• Utilized geometrical arguments to validate the Glansdorff-Prigogine universal criterion of evolution.
• Derived new closure equations for nonlinear corrections to Onsager transport coefficients.

Main Results:

• Demonstrated that the thermodynamic space geometry is non-Riemannian, approaching Riemannian at high entropy production.
• Recovered established transport equations in the high entropy production limit.
• Provided a framework applicable to magnetically confined plasmas, materials with coupled gradients, and chemical reactions.

Conclusions:

• The modified TFT provides a more general framework for non-equilibrium systems.
• The approach is particularly relevant for understanding transport in tokamak plasmas, where local equilibrium is not fully established.
• The derived nonlinear relations are essential for accurate modeling of complex thermodynamic processes.