Why is thermal energy treated differently than other kinds of energy?

[Andrew Mason]

In principle, we could completely ignore statistical mechanics and thermal energy, and explain everything as you would like, in terms of causal directional forces. In fact, that would be more correct to do. But to do that, we would need to keep track of every atom, and for systems with a huge number of atoms (typically $10^{23}$) we cannot do that in practice. So it is for purely practical reasons that we abandon this more correct approach based on causal directional forces, and approximate it with the statistical approach. The price payed by using the statistical approximation is precisely the loss of the causal description you are talking about. So to make the long story short, it's not that thermal phenomena are fundamentally different from all other physical phenomena. Instead, it's that the thermal description is just an approximation, used for the sake of simplification of the system that otherwise is very complicated. It's a clever trick, that reduces a system with a huge number of degrees of freedom to a simplified theory dealing with only a few degrees of freedom.

All good points. But I might take a bit of an issue with the suggestion that the statistical methods are just an approximation.

Since thermodynamics was developed before atomic theory and was considered to be a separate field of physical science, the OP is correct in their observation that thermodynamics and Newtonian mechanics were distinct. Statistical mechanics and atomic theory made that distinction disappear by explaining thermodynamic states and processes in terms of the underlying mechanical interactions of particles.

As you point out, statistical mechanics assumes large systems of particles (in the order of Avogadro's number of particles). And since it applies only to such systems in thermodynamic equilibrium and to thermodynamic processes between states of thermodynamic equilibrium for these systems its application is limited. But statistical mechanics is very accurate in these applications.

Where classical statistical methods break down is where temperatures are very low and quantum effects predominate. That is where classical statistical mechanics don't work and have to be replaced by quantum statistical mechanics. And when that occurs, quantum statistical mechanics is very accurate (again for systems of large numbers of particles).

So it seems to me that statistical methods are only an approximation of underlying behaviour of large numbers of particles if the accuracy required is beyond than anything physically measureable.

AM