Thermodynamics of anomaly-driven cosmology

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 the super-Yang?Mills theory. This correspondence allows for a thermodynamic description of the dynamics of the Randall?Sundrum braneworld scenario.