  The cosmological Friedmann equation sourced by the trace anomaly of a
conformal field theory that is dual to the five-dimensional Schwarzschild-AdS
geometry can be derived from the first law of thermodynamics if the apparent
horizon of the boundary spacetime acquires a logarithmically-corrected
Bekenstein-Hawking entropy. It is shown that such a correction to the entropy
can arise when the generalized uncertainty principle (GUP) is invoked. The
necessary condition for such a thermodynamic derivation directly relates the
GUP parameter to the conformal anomaly. It is consistent with the existence of
a gravitational cutoff for a theory containing $n$ light species. The absolute
minimum in position uncertainty can be identified with the scale at which
gravity becomes effectively five-dimensional.
