OK I rephrase, and Gulfstream is writing it the same way.
For A specific fuel density, temperature is the limiting factor, and Gulfstream chose to limit the amount of fuel in the tanks to permit expansion. ( not Dassault on the F2TH), as a consequence for the same "quality" of fuel, the range will be the same for the volume loaded.
As far as thermodynamic is concerned, yes you are right in a closed system ( Brayton cycle), which is NOT the case as heat exchange occurs between the fuel and the exterior.
The engine fuel metering are sending volume of fuel through the nozzles, not weight of fuel, the indicated Lbs/hrs is a computed information based on standard value ( may be today the FQMC are smart enough to read the SG and such and give a better insight to the crews.
I only flew the G 2, long time ago, and thanks for the reading..