The problem of galaxy formation and its dependence on thermodynamic properties is addressed by using Eulerian hydrodynamic numerical simulations of large scale structure formation. Global galaxy properties are explored in simulations including gravitation, shock heating and cooling processes, and following self-consistently the chemical evolution of a primordial composition hydrogen-helium plasma without assuming collisional ionization equilibrium. The galaxy formation model is mainly based on the identification of converging dense cold gas regions. We show that the evolution at low redshift of the observed cosmic star formation rate density is reproduced, and that the galaxy-like object mass function is dominated by low-mass objects. The galaxy mass functions are well described by a two power-law Schechter function whose parameters are in good agreement with observational fits of the galaxy luminosity function. The high-mass end of the galaxy mass function includes objects formed at early epochs and residing in high-mass dark matter halos whereas the low-mass end includes galaxies formed at later epochs and active in their ``stellar'' mass formation. Finally, the influence of two other physical processes, photoionization and non-equipartition processes between electrons, ions and neutrals of the cosmological plasma is discussed and the modifications on galaxy formation are examined.