Equivalence of the modified gravity equation to the Clausius relation Kazuharu Bamba, Chao-Qiang Geng, Shin'ichi Nojiri and Sergei D. Odintsov EPL, 89 5 (2010) 50003 Published online: 18 March 2010 DOI: 10.1209/0295-5075/89/50003