Entropy Production of Open Quantum System in Multi-Bath Environment
  We study the entropy production of an open quantum system surrounded by a complex environment consisting of several heat baths at different temperatures. The detailed balance is elaborated in view of the distinguishable channels provided by the couplings to different heat baths, and a refined entropy production rate is derived accordingly. It is demonstrated that the entropy production rates can characterize the quantum statistical property of the baths: the bosonic and fermionic baths display different behaviors in the high-temperature limit while they have the same asymptotic behavior at low temperature. 
Cheng-Yun Cai, Sheng-Wen Li, Xu-Feng Liu, C. P. Sun
cond-mat.stat-mech quant-ph