Irreversible Thermodynamics of the Universe: Constraints from Planck   Data
  The present work deals with irreversible Universal thermodynamics. The homogenous and isotropic flat model of the universe is chosen as open thermodynamical system and non-equilibrium thermodynamics comes into picture due to the mechanism of particle creation. For simplicity, entropy flow is considered only due to heat conduction. Further, due to Maxwell-Cattaneo modified Fourier law for non-equilibrium phenomenon, the temperature satisfies damped wave equation instead of heat conduction equation. Validity of generalized second law of thermodynamics (GSLT) has been investigated for Universe bounded by apparent or event horizon with cosmic substrutum as perfect fluid with constant or variable equation of state or interacting dark species. Finally, we have used three Planck data sets to constrain the thermal conductivity \lambda and the coupling parameter b^2. These constraints must be satisfied in order for GSLT to hold for Universe bounded by apparent or event horizons. 
Subhajit Saha, Atreyee Biswas and Subenoy Chakraborty
gr-qc