Lagrangian field theory of reaction-diffusion

Area of Science:

• Theoretical Physics
• Mathematical Biology
• Chemical Kinetics

Background:

• Reaction-diffusion systems are fundamental in modeling various phenomena, from biological pattern formation to chemical reactions.
• Traditionally, these systems were not considered derivable from a Lagrangian field theory.
• A known link exists between quantum mechanics and diffusion processes, suggesting potential theoretical connections.

Purpose of the Study:

• To implement a Lagrangian approach for general nonlinear reaction-diffusion systems.
• To demonstrate that such systems can be described by a Lagrangian field theory.
• To define and derive global conserved observables using Nöther's theorem.

Main Methods:

• Development of a general Lagrangian formulation for nonlinear reaction-diffusion equations.
• Application of Nöther's theorem to identify conserved quantities within the derived Lagrangian framework.
• Validation of the approach for arbitrary nonlinear reacting-diffusing systems.

Main Results:

• A novel Lagrangian field theory framework is established for nonlinear reaction-diffusion systems.
• Global conserved observables are successfully defined and derived using Nöther's theorem.
• The study overcomes the commonly accepted limitation regarding the Lagrangian description of these systems.

Conclusions:

• The Lagrangian approach is feasible and effective for general nonlinear reaction-diffusion systems.
• Nöther's theorem provides a powerful tool for identifying conserved quantities in these systems.
• This work opens new avenues for theoretical analysis and understanding of complex reacting-diffusion phenomena.