There is a phenomenological and a conceptual structure of physics, which are mutually dependent on each other. This results into regional disciplines of physics, where physics at large scale decouples from the physics at a smaller scale accompanied by different degrees of freedom and different dynamics:

In classical mechanics one deals with three scales according to its three basic measurements: distance D, time T, mass M. In non-relativistic quantum theory and classical relativity it has two scales: D & T resp. D & M (mass M can be expressed through T & D using the Planck constant resp. T can be expressed via D using the speed of light). In relativistic quantum theory there is only one scale: distance D, (DeP) p. 551.


Challenges ...

a. ... in current thermomechanics / thermodynamics

Thermomechanics deals with thermal and mechanical process (Brown motion). Thermodynamics dealing with the concepts of temperature, pressure, and volume is governed by four principles, (1) thermal equilibrium, (2) energy conservation, (3) entropy, (4) unattainable absolute zero point. In all cases only closed energetical system are considered.

There is, essentially, only one problem in statistical thermodynamics: to determine the distribution of an assembly of  identical systems over the possible states in which this assembly can find itself, given that the energy of the assembly is a constant. The idea is that there is weak interaction between them, so weak that one can speak of the „private“ energy of every one of them and that the sum of their „private“ energies has to be equal E. The distinguished role of the energy is, therefore, simply that it is a constant of the motion – the one that always exists, and, in general, the only one, (ScE) pp. 1-2.

b. ... in current quantum mechanics / quantum dynamics

Quantum mechanics is concerned with states and process of matter. Quantum dynamics is concerned with motions and interactions of closed quantum systems over time. Aditionally to matter it deals with the concept of fields. Accordingly, there are decoupled matter and interaction objects (fermions & bosons) for each quantum dynamic phenomenon or modelling case (QED (interaction between matter and light), QCD, QFD, Higgs). The three SMEP systems show similar gauge symmetry properties. The Higgs system is incompatible with the SMEP systems.

c. ... in current galactic mechanics /  galactic dynamics

There seems to be no clear differentiation between galactic mechanics and galactic dynamics. Most probably, because there is no closed system to be considered. A similar unspecified situation exists in case of all „theories“ based on the so-called Big Bang „Theory“ („even though it was the biggest black hole ever, it exploded out of nowhere“, (DeK); „producing an universe resembling the one in which we live with a probability of the inverse of 10 exp (10 exp (123))“, (PeR) p. 444). The probability that God made it within six days including a beer to celebrate the work at the seventh day seems to be more likely, especially as this scenario provides also an explanation of the existence of organisms on Earth. In any case, the most mathematical tool being applied so far in galactic dynamics are ordinary differential equations depending from a „cosmic time“ parameter and a few cosmic constants like the Hubble constant.

Galactic (stellar) dynamics is the principle tool for the study of the motion of a large number of point masses orbiting under the influence of their mutual self-gravity, (BiJ) xiv. In its purest form, Landau damping represents a phase-space behavior peculiar to collisionless systems. The dynamic plasma characteric, the Landau damping also exist in the interactions of stars in a galaxy at the Lindblad resonances of a spiral downsity wave. Such resonances in an inhomogeneous medium can produce wave absorption (in space rather than in time), which does not usually happen in fluid systems in the absence of dissipative forces (an exception in the behavior of corotation resonances for density waves in a gaseous medium), (ShF) p. 402.