We place the Landau theory of critical phenomena into the larger context of multiscale thermodynamics. The thermodynamic potentials, with which the Landau theory begins, arise as Lyapunov like functions in the investigation of the relations among different levels of description. By seeing the renormalization-group approach to critical phenomena as inseparability of levels in the critical point, we can adopt the renormalization-group viewpoint into the Landau theory and by doing it bring its predictions closer to results of experimental observations.

Department of Mathematics FNSPE Czech Technical University Prague Trojanova 13 12000 Prague Czech Republic

École Polytechnique de Montréal C P 6079 suc Centre Ville Montréal QC H3C 3A7 Canada

Mathematical Institute Faculty of Mathematics Charles University Sokolovská 83 18675 Prague Czech Republic

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The Statistical Foundations of Entropy