  The thermal history of the Universe is introduced within the Debye
Gravitational Theory (DGT), a thermodynamic theory of induced gravity, and
allows to obtain the evolution of systems with the redshift. DGT reproduce the
ESO VLT observations, showing falling outer rotation curves for galaxies at
redshift above 0.77. A scaling law is observed in the radial acceleration
relation (RAR) of galaxies. For accelerations smaller than $\sim
10^{-10}ms^{-1}$ the observed acceleration $g_{obs}$ decreases more slowly than
acceleration generated by the baryonic mass $g_{bar}$, following always the
relation $g_{obs} \sim \sqrt{g_{bar}}$. The RAR does not care about the
specific properties of the galaxy, the relation exists in nearby high-mass
elliptical and low-mass spheroidal galaxies. In this paper, through a
straightforward analysis, we show that according to DGT, the RAR scaling law
observed in nearby galaxies is broken, when are considered distant galaxies.
The extreme case happen for galaxies at redshift above 0.77, because according
to DGT, the galaxies have declining rotation curves, and the rotation velocity
falling faster than the Keplerian-law curve. Then in this case $g_{obs}$
decreases more faster than $g_{bar}$, this means that $g_{obs}$ is
systematically lower than $g_{bar}$. We show that DGT prediction for the RAR of
galaxies at high redshift is in agreement from those obtained from the falling
rotation curves observed by VLT telescope.
