Statistical behaviour of a proxy of the entropy production rate of the solar photosphere

The solar photosphere provides an incomparable laboratory to study turbulent convection in a dissipative non-equilibrium system. The evaluation of the entropy production rate on the solar photosphere and its probability distribution are the key issues for studying the non-equilibrium dynamics of the solar convection. The local entropy production rate is not offhandedly measurable on the solar photosphere, but it can be easily evaluated using the vertical heat flux as a proxy, which is given by the product between the line-of-sight velocity and the surface temperature. In this work, we present some preliminary results on statistics of the local entropy production rate via the vertical heat flux, using line-of-sight velocity and temperature maps of the solar photosphere which are derived from high-resolution spectro-polarimetric data making use of the Center of Gravity Method and the Stefan-Boltzmann law.