Cartan's Magic Formula

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.
TO test for reversibility, check to see if Q^dQ= 0. If not true, the process is irreversible.

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


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Last update 01/23/2009
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