Thermodynamics and Mechanics without Statistics.
A major objective is to find a method of determining when a process acting on a physical system is irreversible in the thermodynamic sense. The classic thermodynamic definition of irreversibility is that the inexact differential of Heat, Q, does not admit an integrating factor (the Temperature T). By using differential forms this concept can be translated into the statement that the 1-form of heat does not satisfy the Frobenius integrability theorem.
Herein it is assumed that the physical system is described by a 1-form of
Action, and that a physical process can be described by a vector field. Then
the physical system is propagated by means of the Lie derivative with respect to
V to produce a 1-form of Heat.
It turns out that irreversible processes are artifacts of 4 dimensions or more.
On a 4 dimensional space the direction field of the Topological Torsion vector
defines irreversible processes.
The second download exhibits a poster presented at the Gordan conference on Modern Developments in Thermodynamics in Italy, April 18-22, 1999