Hierarchies of energy conversion processes III. Why are onsager equations reciprocal? The euclidean geometry of fluctuation-dissipation space

Abstract

The present communication shows the relationship between the simple linear energy conversion processes introduced in parts I and II and the n -dimensional geometry of Onsager thermodynamics. It is shown that Network Thermodynamics corresponds to a state by state imbedding of the euclidean Onsager geometry in a geometry of n ( n + 1)/2 dimensions or higher. The end result of this process is the demonstration that reciprocity is implicit in the geometrical definition of the theory. In particular, it is indicated how the principle of detailed balance corresponds to Kirchhoff's voltage laws in network terms. It is also shown that the coupling coefficient q is simply an angle between vectors in this geometry, so that the problem of energy conversion in Onsager thermodynamics is reduced to the variations in these angles. This representation provides a logical relationship between (lumped parameter) network thermodynamics and differential geometry, thus placing this more practical viewpoint on an equal footing with bond graph Network Thermodynamics.