Maybe I can give a layman's perspective on this. I'm not saying I'm right on the money but this is how I understand it and anyone like Gaspar who might be able to correct me please do so, I'd like to know for sure myself.

Turbine engines have two major operational limitations. RPM and Temperature. One can set thrust pretty closely by RPM, but not exactly. One can even set thrust by temperature, but again not exactly and probably not as closely as using RPM due to variable levels of wear and tear in the temp probes. But you can set thrust using each one of those to variable levels of accuracy and that gives us insight to what's going on inside a turbine.

RPM is a secondary thrust measurement value really - the true measurement of thrust is the pressure ratio between inlet and exhaust pressure, and that brings the chemical reaction of the burned fuel into the equation along side of the basics of the engine RPM. So the specific energy of the fuel comes into play - in addition to spinning the turbine and the compressor wheel it's adding dynamic mass and acceleration (force) to the exhaust. A "good" engine and "good" fuel can make more thrust at the same RPM than an identical model "sick" engine, for example, or one with "mild" fuel contamination.

In many full size jet engines, "EPR" (engine pressure ratio) is used, as a cockpit display (often), but always by the engine control unit directly, to measure and control desired thrust. Some engines (some P&W's for example) use N1 or "main rotor RPM" as a primary thrust setting indicator for operational simplicity. A known down side to this (splitting hairs on a normally decent day) is the fact that a certain N1 or rotor speed is not always giving an exact measured thrust. On a bad day, simply setting an "N1" without good situation awareness can get you nowhere close to the thrust setting thought to be set. But that's beyond the scope here. Where as, a specific "EPR" setting (for the many engines that use EPR as the primary thrust setting indication) is in fact giving true thrust -EPR is EPR, and that means specific thrust.

So, N1's, or rotor speeds, are widely understood to be capable of small variances for a given actual thrust achieved in normal operations.

This is not to confuse the above with the simple case of a difference in density altitude. For example, on a hot day at 150K (let's say that's the Max RPM on the model engine ECU) you may get 25 pounds of thrust. And on a cold day at 150K, you may get 27.5 pounds of thrust. (Assuming you don't reach the EGT limit first in either case). Or on a hot day on an older engine you may reach the EGT limit at only 147K, and have just 24 pounds of thrust. Again, this is a little different than the question of a different fuel chemistry giving more or less thrust to an engine.

So, engine thrust on a specific day, temperature and altitude is not specifically dependent on specific rotor RPM, though it is very closely linked. It is reasonable to expect minor increases (or decreases) in thrust (or EPR) at specific RPM for either environmental reasons or chemical reasons (diesel).