From Statistical Mechanics to Process Control: A Tutorial

A system-theoretic basis for process control is developed using statistical mechanics as our point of departure. Specifically we show that a thermodynamic system can be discussed within the framework passive systems theory. Using Boltzmann's definition entropy S = kB ln(Ω) and assuming distribution states uniformly distributed close to equilibrium manifold demonstrate existence Lyapunov function based on concept available work. The LaSalle invariance principle now applies conclude microscopic (quantum) state converges an ω-limit set manifold. support measure V, interpreted volume system, defines phase in multi-phase system. To connect such ideas with define (approximate) balance equations, force, flux variables.