It's in the physics. Energy is force (aka weight) x distance. Since you're moving the same amount of weight (yours) over say, a mile, regardless of whether you're running or walking, you're expending the same calories. If you increase your speed you'd be burning more calories per minute because you take less time to complete the mile. So, running for 30 minutes burns more calories than walking for 30 minutes because you're covering a greater distance. But running for 5 miles and walking for 5 miles burns an identical amount of energy.