Review of extremum postulates

• Thermodynamic equilibrium is a multiscale illusion.
• Extrema of entropy production as a clash of statistical and continuum mechanics.
• Extrema of entropy production as uncertainty principle in path dependent processes.
• Thermodynamic homogenization of dissipative processes provides novel material laws.
• Thermodynamic upscaling breaks down the dimensionality of the system.

Variational principles applied to the time derivative of the second law of thermodynamics have led to significant progress of our understanding of dynamic systems. Prigogine proved that chemical species dynamically form an oscillatory pattern of minimum of entropy production, MinEP. The opposite MaxEP 3 postulate forms the foundation of continuum mechanics. The topic of which extremum is valid under what conditions is still subject of a heated debate. We posit here that the two principles emerge from a different spatial/temporal homogenisation technique. MaxEP derives from a macroscopic, continuum view of a non-equilibrium stationary state and MinEP from a microscopic discrete view of stability of a dissipative system. When both limits coincide the system can be represented by an upscaled state with reduced degrees of freedom.