Which specific subdivision of the nervous system calms the body after strenuous physical activity?

The answer to this question would be: parasympathetic division

Parasympathetic nervous is part of the autonomous nervous system. In the autonomous nervous system, the sympathetic system is used when you enter the "fight or flight" mode. In this case, the body will be prepared to be able to take a decision as quickly as possible in a strenuous state. The nervous also cause an increase in the heart and breathing rate to increase body capability.
Parasympathetic is the opposite of it which was activated to calm the body so it can maintain the normal body function.