In this review article an account will be given of themes that are more or less connected with the relation between general stochastic measures in general statistics and thermodynamics. First, these measures and their correspondence in equilibrium thermodynamics will be represented. Then the extension to nonequilibrium thermodynamics and examples on different levels of description will be considered. A generalisation of the specific heat as an outstanding representive of a whole class of independent measures will be considered. The critical behaviour of this quantity in nonequilibrium phase transition will be analysed for several models. These are the main lines round that gather special themes.