  The Friedmann equations of general relativity can be derived from the first
law of thermodynamics when the entropy of the apparent horizon of a spatially
isotropic universe is given by the Bekenstein-Hawking entropy. We point out
that if the entropy of the apparent horizon receives a logarithmic correction,
the first law of thermodynamics leads to a modified Friedmann equation which
corresponds precisely to the time-time component of the semi-classical Einstein
field equations sourced by the trace anomaly of ${\cal{N}}=4$ U(N)
super-Yang-Mills theory. This correspondence allows for a thermodynamic
description of the dynamics of the Randall-Sundrum braneworld scenario.
