(Ken S. Tucker) wrote:
The quantity T is identitied as the stress tensor of the system,
and e as the system's internal energy. They are related by:
1/2 trace(T) = rho e.

In fact, this is true for monoatomic gases. For diatomic and
polyatomic gases, there is an additional component to e that
does not arise from the 1/2 the trace of T.

Agreed, would you say these "additional components"
are antisymmetric and or nonorthogonal components
off the trace, where the trace T solves only mono's?

e and trace(T) are invariant under Galilean transformations, and
under the "scale" or "additivity" transformation. So, the
difference (e - 1/2 trace(T)) persists at all levels: microscopic
and macroscopic, and is intrinsic.

So, if the continuum decomposes into fundamental subsystems (the
"particles") the difference (e - 1/2 trace(T)) for that
subsystem represents a source of energy arising from intrinsic
degrees of freedom OTHER than the translational degrees.

It's direct evidence of the existence of non-translational
degrees of freedom in particles (i.e., spin); and is entirely
non-classical in origin.

In fact, for polyatomic gases, the e WILL actually be
1/2 trace(T) at low enough temperatures; because the other
degrees of freedom are frozen out. For diatomic gases, it pushes
up to 5/6 trace(T) past a certain critical temperature, as the
other degrees of freedom "thaw" out; and for polyatomic gases,
up to trace(T).