In this talk I will discuss some relation between thermodynamics formalism and bounded cohomology. The goal is to show how quasi-morphisms on some groups relate to quasi-cocycles of certain dynamical systems. Then one can analyze the former using the latter. The latter can be related to functions with the Bowen property and in some cases shown to be trivial, giving another proof of a result of Burger and Monod. This is joint work with Pablo Carrasco.