Constitutive and dynamic relations for friction coefficient are presented. A first thrust combines the laws of thermodynamics to relate heat, energy, matter, entropy, and work of forces. The equation sums multiple terms—each with a differential of a variable multiplied by a coefficient—to zero. Thermodynamic considerations suggest that two variables, internal energy and entropy production, must depend on the others. Linear independence of differentials renders equations that yield thermodynamic quantities, properties, and forces as functions of internal energy and entropy production. When applied to a tribocontrol volume, constitutive laws for normal and friction forces, and coefficient of friction are derived and specialized for static and kinetic coefficients of friction. A second thrust formulates dynamics of sliding, with friction coefficient and slip velocity as state variables. Differential equations derived via Newton's laws for velocity and the degradation entropy generation (DEG) theorem for friction coefficient model changes to the sliding interface induced by friction dissipation. The solution suggests that the transition from static to kinetic coefficient of friction with respect to slip velocity for lubricant starved sliding is a property of the motion dynamics of sliding interacting with the dynamics of change of the surface morphology. Finally, sliding with stick-slip was simulated to compare this model to others.

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