Entropy Production and Irreversible Processes 262 Entropy Production and Irreversible Processes - from the perspective of continuous topological evolution

A concept of entropy production associated with continuous topolog-ical evolution is deduced (without statistics) from the fact that Cartan-Hilbert 1-form of Action defines a non-equilibrium symplectic system of Pfaff Topological dimension 2n+2. The differential entropy, dS, is composed of the interior product of the non-canonical components of momentum with the components of the differential velocities. An irreversible process can describe entropy production in terms of continuous topological evolution to non-equilibrium but stationary states. An equilibrium system can be defined topologically as a Lagrange sub-manifold of the 2n+2 topological space, upon which the change in entropy by continuous topological evolution is zero, dS {equil} =0. ––––––––––––––––––––––––––––––––––––— 1 A Topological Perspective In this article, non-equilibrium thermodynamics will be studied from the perspective of continuous topological evolution, using methods based upon Cartan's theory of exterior differential forms. Discontinuous processes and statistical methods are, more or less, ignored, for a method has been found to distinguish between the dynamics of reversible and irreversible processes acting on non-equilibrium systems. The title emphasizes that this article