In the study of Lagrangian systems with constraints it becomes evident that the
kinematic assumptions :
dx - Vdt = 0
dV - Adt = 0
are strong topological constraints on the domain of interest. Suppose that these differential 1-forms are not perfect, but have (perhaps small) fluctuations. The non-zero RHS may have physical significance.
So reconstruct a Lagrange Action principle and use Lagrange multipliers to
include the constraints:
A = L(x,v,t)dt + alpha ( dx-Vdt) +beta (dV-Adt)
Such additions change the Pfaff dimension and the interpretation of the analysis
In summary it would appear that there exist certain terms (like a pressure gradient) that are due to the anholonomic fluctuations in dx-Vdt.
Similarly there exist certain terms (like a temperature gradient) that are due
to the anholonomic fluctuations in dV-Adt.
It is suggested that the source of the Casimir pressure is ultimately due to
such anholonomic fluctuations in position, and the Davies-Unruh temperature is
due to such anholonomic fluctuations in velocity.