Use lower case for all laws and formulas, unless named after a discoverer. Separate co-discoverers with an en dash. However, each law should be researched to determine its history:
Carathéodory’s formulation Clausius–Kelvin–Planck way Knudsen gas
Joule–Thomson expansion Massieu functions
but
adiabatic gas law zeroth, first, second and third laws of thermodynamics local thermodynamic equilibrium