  We present for the neutron-star low-mass X-ray binary 4U 1636$-$53, and for
the first time for any source of kilohertz quasi-periodic oscillations (kHz
QPOs), the two-dimensional behaviour of the fractional rms amplitude of the kHz
QPOs in the parameter space defined by QPO frequency and photon energy. We find
that the rms amplitude of the lower kHz QPO increases with energy up to
$\sim12$ keV and then decreases at higher energies, while the rms amplitude of
the upper kHz QPO either continues increasing or levels off at high energies.
The rms amplitude of the lower kHz QPO increases and then decreases with
frequency, peaking at $\sim 760$ Hz, while the amplitude of the upper kHz QPO
decreases with frequency, with a local maximum at around $\sim 770$ Hz, and is
consistent with becoming zero at the same QPO frequency, $\sim1400$ Hz, in all
energy bands, thus constraining the neutron-star mass at $M_{NS} \leq 1.6
M_{\odot}$, under the assumption that this QPO reflects the Keplerian frequency
at the inner edge of the accretion disc. We show that the slope of the rms
energy spectrum is connected to the changing properties of the kHz QPOs in
different energy bands as its frequencies change. Finally, we discuss a
possible mechanism responsible for the radiative properties of the kHz QPOs
and, based on a model in which the QPO arises from oscillations in a
Comptonising cloud of hot electrons, we show that the properties of the kHz
QPOs can constrain the thermodynamic properties of the inner accretion flow.
