Robert M. Kiehn
Physics Department, University of Houston, Houston, TX 77004 USA.
http://www.cartan.pair.com
Received: 19 November 2003 / Accepted: 4 May 2004 / Published: 17 May 2004
Abstract: A concept of entropy production associated with continuous topological 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 submanifold of the 2n+2 topological space, upon which the change in entropy by continuous topological evolution is zero, dSequil=0.
Keywords: Entropy production; Irreversible processes; Pfaff topological dimension; Cartan's Magic formula; Decay to stationary states far from equilibrium.