The second of these divisions refers to the theory of heat,…

The second of these divisions refers to the theory of heat, which is now understood to be a kind of motion among bodies that is too small to be directly observed. In statistical mechanics, a body is understood to be more than simply a position and momentum. Instead it is a probability distribution over a range of positions and momenta that represents many small particles.
The connection between heat and motion took a long time for people to understand. Before it was understood, the principle of the conservation of energy, which is now central to all physics, could not be understood because it appeared that two bodies could interact in a way that caused both of them to slow down until they were at rest relative to one another. It is now understood that the coherent motion of the two bodies is converted into incoherent motion of their particles, which is experienced by us as heat.
In non-thermal physics, the notion of entropy does not exist.
There is a theory called thermodynamics which models heat as a fundamental quantity, like mass or charge. This theory is deterministic, like everyday classical physics. However,