I have no idea if this site is reliable, but I liked this part.
Quran restores soul calmness:
The results of researches conducted over a group of volunteers from USA who were subject to a recitation of the Holy Quran were striking. A trace of a tranquilizing effect was recorded at a whole rate of 97%. Although many of these volunteers do not know Arabic, yet involuntary physiological changes that led notably to alleviate the acuity of tension they had before were observed in their nervous systems. Furthermore, an experiment of EEG during Quran rehearsal revealed that while listening to Quran, the encephalic waves moved from the fast pattern of vigilance (12-13) wave/ second to the slow pattern (8-18) wave/ second; indicating the state of deep calmness. Non-Arabic speaking persons felt reassured, quiet, and complacent during the process of listening to Quranic verses, in spite of their inability to understand the meanings. This is one of the miracles of the Holy Quran. The Prophet revealed that miracle when saying;
“No people assembled in one of the houses of Allah (mosques), and recite and study the Book of Allah (among themselves), except that tranquility would prevail over them, and mercy would encompass them, and the angels would surround them, and Allah would make a mention of them in the presence of those near Him.”
So from the above it's indicative of being in a calm state, so do you really want to jog whilst in a calm state? if you get what I mean, coz they're like two opposites innit?
I don't know though, sorry. I couldn't find any fatwas either.