Sorry I only have a Biology degree, but hopefully this helps:
Higher octane ratings correlate to higher activation energies: This being the amount of applied energy required to initiate combustion. Since higher octane fuels have higher activation energy requirements, it is less likely that a given compression will cause uncontrolled ignition, otherwise known as autoignition or detonation.
The compression ratio is directly related to power and to thermodynamic efficiency of an internal combustion engine (Otto-cycle). Engines with higher compression ratios develop more area under the Otto-Cycle curve, thus they extract more energy from a given quantity of fuel.
During the compression stroke of an internal combustion engine, as the air / fuels mix is compressed its temperature rises (PV=nRT).
A fuel with a higher octane rating is less prone to auto-ignition and can withstand a greater rise in temperature during the compression stroke of an internal combustion engine without auto-igniting, thus allowing more power to be extracted from the Otto-Cycle.
If during the compression stroke the air / fuel mix reaches a temperature greater than the auto-ignition temperature of the fuel, the fuel self or auto-ignites. When auto-ignition occurs (before the piston reaches the top of its travel) the up-rising piston is then attempting to squeeze the rapidly expanding (exploding) fuel charge. This will usually destroy an engine quickly if allowed to continue.
There are two types of induction systems on internal combustion engines: Normally aspirated engine (air is sucked in using the engine's pistons), or forced induction engines (see supercharged or turbocharged engines).
In the case of the normally aspirated engine, at the start of the compression stroke the cylinder air / fuel volume is very low, this translates into a low starting pressure. As the piston travels upward, a compression ratio of 10:1 in a normally aspirated engine will most likely not start auto-ignition. But 11:1 may. In a forced induction engine where at the start of the compression stroke the cylinder pressure is already raised (having a greater volume of air / fuel) Exp. 2 Bar (14.7Psi), the starting pressure or air / fuel volume would be 2 times that of the normally aspirated engine. This would translate into an effective compression ratio of 20:1 vs. 10:1 for the normally aspirated. This is why many forced induction engines have compression ratios in the 8:1 range.
Many high-performance engines are designed to operate with a high maximum compression, and thus demand fuels of higher octane. A common misconception is that power output or fuel efficiency can be improved by burning fuel of higher octane than that specified by the engine manufacturer. The power output of an engine depends in part on the energy density of the fuel being burnt. Fuels of different octane ratings may have similar densities, but because switching to a higher octane fuel does not add more hydrocarbon content or oxygen, the engine cannot develop more power.
However, burning fuel with a lower octane rating than that for which the engine is designed often results in a reduction of power output and efficiency. Many modern engines are equipped with a knock sensor (a small piezoelectric microphone), which sends a signal to the engine control unit, which in turn retards the ignition timing when detonation is detected. Retarding the ignition timing reduces the tendency of the fuel-air mixture to detonate, but also reduces power output and fuel efficiency. Because of this, under conditions of high load and high temperature, a given engine may have a more consistent power output with a higher octane fuel, as such fuels are less prone to detonation. Some modern high performance engines are actually optimized for higher than pump premium.
Most fuel filling stations have two storage tanks (even those offering 3 or 4 octane levels): those motorists who purchase intermediate grade fuels are given a mixture of higher and lower octane fuels. "Premium" grade is fuel of higher octane, and the minimum grade sold is fuel of lower octane. Purchasing 91 octane fuel (where offered) simply means that more fuel of higher octane is blended with commensurately less fuel of lower octane, than when purchasing a lower grade. The detergents and other additives in the fuel are often, but not always, identical.
---------- Post added at 02:33 PM ---------- Previous post was at 01:38 PM ----------
I will also add, that 07+ 5.3L engines are at a higher compression (10:1) and can not run efficiently on 87.
The OP will probably see 14MPGs in the city alone, just by running 89.