Why does fuel consumption decrease with increasing aircraft altitude? I have a chart where the thrust ($F$) and the thrust-specific fuel consumption (TSFC) are plotted against the aircraft flying speed, for several altitudes (i.e. sea level, 3000 meters and 11000 meters). This is for a generic turbojet.



I don't know the source of the image, I apologize for that.

At the left, we see that the thrust decreases with altitude. At the right, we observe that the TSFC actually decreases with altitude as well.

However, I think this is counter-intuitive. I understand that $F$ decreases with altitude, since density (and therefore mass flow rate) decreases when the airplane goes up.

What I don't understand is that the TSFC, defined as: $$\text{TSFC}\equiv\dfrac{\text{fuel mass flow rate}}{F}$$ decreases with altitude. In other words, the higher we fly, the more thermodynamically-efficient the airplane is. How does that happen?

From a pure mathematical point of view, it doesn't make sense that TSFC decreases with altitude since, following the aforementioned formula, $F$ is decreasing, which leads me to think that the fuel mass flow rate diminishes with altitude faster than thrust.

In a nutshell: why does the TSFC decreases with the flying altitude, having the last equation into consideration?
I can't provide the math, but yes, this is correct. Fuel flow decreases as air density decreases. The engine becomes more efficient because of the greater temperature differential between inlet and exhaust gases combined with the lower fuel flow.