A general information theoretical proof for the second law of thermodynamics

We show that the conservation and the non-additivity of information, together with the additivity of entropy makes entropy increase in an isolated system.The collapse of the entangled quantum state offers an example of the information non-additivity. Nevertheless, the later is also true in other fields, in which the interaction information is important. Examples are classical statistical mechanics, social statistics and financial processes. The second law of thermodynamics is thus proven in its most general form. It is exactly true, not only in quantum and classical physics but also in other processes in which the information is conservative and non-additive.