The ideal gas law;
P*V = k*N*T
k; Bolzmann constant.
P; Pressure
V; Volume
N; Number of particles
T; Temperature
Map the four thermodynamic variables to physical categories;
(Energy,Momentum)
(Time,Space)
(Mass,Charge)
(Gravity,Boson)
The symmetries reflect each other;
((P,V),(N,T))
(((Energy,Momentum),(Time,Space)),((Mass,Charge),(Gravity,Boson)))
The choice of the physical categories is also supported by the common (1,3) symmetry;
Momentum; (Px,Py,Pz)
Space; (x,y,z)
Charge; (Electric,Weak,Color)
Boson; (Light,Weak,Gluon)
Mass and Energy are scalars, Time and Gravity are vectors.
The eight physical categories are fully meshed; each is related to the other seven, although the indicated relationships are the strongest. Thus an 8*8 matrix is needed to contain all relationships.