Entropy production and irreversible processes -- from the perspective of continuous topological evolution (Q1769749)

Summary: 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, \(dS_{\{\text{equil}\}}=0\).