Dynamical Casmir effect and Conductivity
  In this paper we find that the second law of thermodynamics requires an upper limit of the conductivity. To begin with we present an ideal model, the cavity with a mobile plate, for studying the thermodynamic properties of radiation field. It is shown that the pressure fluctuation of thermal radiation field in the cavity leads to the random motion of the plate and photons would be generated by dynamical Casimir effect. Meanwhile, such photons obey a non-thermal distribution. Then, to ensure the second law of thermodynamics, there must be a upper limit of the conductivity. 
Xiao-Min Bei and Zhong-Zhu Liu
quant-ph cond-mat.stat-mech