Thermal and hard scales in transverse momentum distributions, fluctuations and entanglement

We analyze the transverse momentum distributions of pp, pPb, XeXe and PbPb collisions at different RHIC and LHC energies and centralities as well as the corresponding distributions for Higgs production decaying into $\gamma\gamma$ and 4l. A simple linear relation is found between the effective thermal temperature and the hard scale, approximately valid for all processes and mainly determined by the hard scale fluctuations. In order to go further, it is shown that the whole spectrum of pp collisions can be described by a single function showing that the thermal temperature is determined solely by the hard scale and its fluctuations. The possible relation between the multiplicities of the soft and hard scales is explored.