Evaluating a proxy of the local entropy production rate on the solar photosphere

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 can be easily evaluated using the vertical heat flux as a proxy, which is given by a product between the line-of-sight velocity and the surface temperature. In this framework, the solar photosphere provides an incomparable laboratory to study turbulent convection in a dissipative non-equilibrium system near a steady state. 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 extracted from spectro-polarimetric data making use of the Center of Gravity Method and the simple black body radiation law.