  The emission mechanism during the prompt phase in gamma-ray bursts (GRBs) can
be investigated through correlations between spectral properties. Here, we
revisit the correlation relating the instantaneous flux, $F$, and the photon
index below the spectral break, $\alpha$, in individual emission pulses, by
studying the 38 most prominent pulses in the Fermi/GBM GRB catalogue. First, we
search for signatures of the bias in the determination of $\alpha$ due to the
limited spectral coverage (window effect) expected in the synchrotron case. The
absence of such a characteristic signature argues against the simplest
synchrotron models. We instead find that the observed correlation between $F$
and $\alpha$ can, in general, be described by the relation $F(t) \propto {\rm
e}^{k\,\alpha(t)}$, for which the median $k = 3$. We suggest that this
correlation is a manifestation of subphotospheric heating in a flow with a
varying entropy. Around the peak of the light curve, a large entropy causes the
photosphere to approach the saturation radius, leading to an intense emission
with a narrow spectrum. As the entropy decreases the photosphere secedes from
the saturation radius, and weaker emission with a broader spectrum is expected.
This simple scenario naturally leads to a correlated variation of the intensity
and spectral shape, covering the observed range.
