  Multiscale thermodynamics is a theory of relations among levels of
description. Energy and entropy are its two main ingredients. Their roles in
the time evolution describing approach of a level (starting level) to another
level involving less details (target level) is examined on several examples,
including the level on which macroscopic systems are seen as composed of
microscopic particles, mesoscopic levels as kinetic theory of ideal and van der
Waals gases, fluid mechanics, the level of chemical kinetics, and the level of
equilibrium thermodynamics. The entropy enters the emergence of the target
level in two roles. It expresses internal energy, that is the part of the
energy that cannot be expressed in terms of the state variables used on the
starting level, and it reveals emerging features characterizing the target
level by sweeping away unimportant details. In the case when the target level
is a mesoscopic level involving time evolution the roles of the energy and the
entropy is taken by two different potentials that are related to their rates.
