  Spontaneous localisation is a falsifiable, phenomenological, mechanism for
explaining the absence of macroscopic position superpositions, currently being
tested for in the laboratory. The theory of trace dynamics provides a possible
theoretical origin for spontaneous localisation. We have recently proposed how
to employ non-commutative geometry to include gravity in trace dynamics, and
suggested the emergence of classical space-time geometry via spontaneous
localisation. In our theory, which we call non-commutative matter gravity, a
black hole arises from the spontaneous localisation of an entangled state of a
large number of `atoms of space-time-matter [STM]'. Prior to localisation, the
non-commutative curvature of an STM atom is described by the spectral action of
non-commutative geometry. By using the techniques of statistical thermodynamics
from trace dynamics, we show that the gravitational entropy of a Schwarzschild
black hole results from the microstates of the entangled STM atoms and is given
(subject to certain assumptions) by the classical Euclidean gravitational
action. This action, in turn, equals the Bekenstein-Hawking entropy
(Area/$4{L_P}^2$) of the black hole. We argue that spontaneous localisation is
related to black-hole evaporation through the fluctuation-dissipation theorem.
