  The velocity and specific entropy of the Chapman-Jouguet (CJ) equilibrium
detonation are shown to be invariant under the same variations of initial
temperature with initial pressure. This leads to additional CJ relations, for
example, for calculating the CJ state -- including the adiabatic exponent --
from the only CJ velocity, without using an equation of state for the
detonation products. For gaseous stoichiometric explosives with ideal products,
numerical calculations with detailed chemical equilibrium confirm the
invariance theorem to $\mathcal{O}(10^{-2}$\% and the additional CJ properties
to $\mathcal{O}(10^{-1}$\%. However, for four liquid carbon explosives, the
predicted CJ pressures are about 20\% higher than the measurements. The
analysis emphasizes the limited physical representativeness of the hydrodynamic
framework of the modelling, i.e. single-phase inviscid fluids at equilibrium
for the initial and final states of the explosive. This invariance may
illustrate a general feature of hyperbolic systems and their characteristic
surfaces.
