Narayanaswamy's 1971 aging theory and material time

Area of Science:

• Statistical Mechanics
• Condensed Matter Physics
• Nonlinear Dynamics

Background:

• Physical aging is a complex, nonlinear phenomenon observed in many systems.
• Narayanaswamy's phenomenological theory describes aging using a linear material-time convolution integral.
• The Bochkov-Kuzovlev nonlinear fluctuation-dissipation theorem provides a theoretical framework.

Purpose of the Study:

• To derive Narayanaswamy's theory of physical aging from fundamental principles.
• To identify the unique definition of material time that satisfies translational invariance.
• To propose computer simulations for testing the consequences of material-time translational invariance.

Main Methods:

• Utilizing the Bochkov-Kuzovlev nonlinear fluctuation-dissipation theorem.
• Assuming material-time translational invariance as the core principle.
• Deriving the mathematical definition of material time based on system path distance.

Main Results:

• Narayanaswamy's aging theory is derived from the fluctuation-dissipation theorem.
• Material time is uniquely defined as the square of the distance traveled by the system.
• The 'unique-triangles property' is identified as a key consequence, linking to spin glass dynamics.

Conclusions:

• The study provides a fundamental basis for Narayanaswamy's aging theory.
• Material-time translational invariance offers a new perspective on physical aging.
• The unique-triangles property offers a geometric interpretation for out-of-equilibrium dynamics.