Thermodynamics/Statistical Mechanics

Thermodynamics
Thermodynamics is the study of energy flow in a system composed of bulk objects. The key variables of interest in thermodynamics are temperature, pressure, volume and entropy (roughly defined as the disorder and available energy in a system).

Thermodynamics is not founded on emergent principles. The individual interactions found in the consitution matter that makes up the objects is ignored and instead the change in the key variables is described in a phenomenologically fashion.

Statistical Mechanics
Statistical mechanics is the study of energy flow in a system composed of an ensemble of interacting particles. The key variables of interest are the same as in thermodynamics.

Unlike thermodynamics, statistical mechanics is entirely emergent. The interactions between individuals are not treated, but the average of all the interactions are treated. This is emergent in the sense that a few interacting particles do not have a temperature, but a large collection of particles do have a temperature that is roughly the average speed of the particles. So, not only is this field emergent but it is the emergent explanation of the much older field of study that is thermodynamics. In this case, by taking an emergent approach the world can be explained in much greater detail and rigor.