Hawking radiation as tunneling and the unified first law of   thermodynamics at the apparent horizon in the FRW universe
  Relations between the tunneling rate and the unified first law of thermodynamics at the apparent horizon of the FRW universe are investigated. The tunneling rate arises as a consequence of the unified first law of thermodynamics in such a dynamical system. The analysis shows obviously how the tunneling is intimately connected with the unified first law of thermodynamics through the principle of conservation of energy. 
Ke-Xia Jiang, San-Min Ke, Dan-Tao Peng and Jun Feng