Just so we have it, the efficiency of any heat engine is limited to the Carnot efficiency:

http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/carnot.htm...

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An internal combustion engine (ICE) uses the Otto cycle:

https://web.mit.edu/16.unified/www/FALL/thermodynamics/notes...

https://www.sciencedirect.com/topics/engineering/otto-cycle

If you click the Read more arrow under 3.4.1 The Efficiency of an Otto Engine, it states that The ideal Otto cycle achieves the Carnot efficiency of an engine working between the maximum, pre-combustion, temperature and the intake temperature. This means that the ideal Otto cycle cannot achieve the Carnot efficiency determined by the highest and lowest temperature during the cycle.

Tlow = T ambient

Thigh = T at highest compression of piston

efficiency ~= 1 - Tlow/Thigh < (Thigh - Tlow)/Thigh = Carnot efficiency

We can find the pre-ignition temperature at maximum compression:

https://www.physicsforums.com/threads/compression-psi-and-te...

T2 = T1 * ((V1/V2)^(y-1)) where y ~= 1.4 for air

So a 14:1 compression ratio at an ambient room temperature of 293 K (20 C or 68 F) gives a pre-combustions temperature of:

T2 = 293 * (14^(1.4-1)) = 842 K (569 C or 1056 F)

So the maximum efficiency (Carnot efficiency) of an Otto cycle 14:1 compression ICE would be less than:

efficiency < (842-293)/842 < 65%

In practice, an ICE might scavange 50% of that due to losses to entropy, friction and hot exhaust at 600 K (about 300 C or 600 F) and end up at 33% efficiency, not counting drivetrain losses of about 15% to get to maybe 28% at the wheels.

That's why ICE vehicles waste around 75% of the fuel's energy or more. Whereas an electric vehicle will be around 90% percent efficient from batteries to motor and around 75% efficient at the wheels, or at least 3 times better than an ICE vehicle.

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A gas turbine uses the Brayton cycle:

https://web.mit.edu/16.unified/www/SPRING/propulsion/notes/n...

The Brayton cycle thermal efficiency contains the ratio of the compressor exit temperature to atmospheric temperature, so that the ratio is not based on the highest temperature in the cycle, as the Carnot efficiency is. For a given maximum cycle temperature, the Brayton cycle is therefore less efficient than a Carnot cycle.

Tlow = T ambient

Thigh = T at highest compression after compressor

effiency ~= 1 - Tlow/Thigh < (Thigh - Tlow)/Thigh = Carnot efficiency

A jet engine might reach 40:1 compression:

T2 = 293 * (40^(1.4-1)) = 1281 K (1008 C or 1846 F)

So the maximum efficiency (Carnot efficiency) of a Brayton cycle 40:1 compression turbine would be less than:

efficiency < (1281-293)/1281 < 77%

In practice, a gas turbine might scavange up to 85% of that and end up at 65% efficiency, not counting generator losses of 5%. But 40-65% overall efficiency is more realistic.

A 45% efficient gas turbine would leave 55% of the energy as waste heat in the exhaust. So a steam turbine scavanging that would only need to be about 35% efficient to reach an overall efficiency of 65%. Depending on exhaust temperature, the article's thermophotovoltaic cells would probably be cheaper and more reliable than additional turbine stages.

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I've never seen a good way to relate Carnot efficiency to quantum efficiency. Thermodynamics measures average emergent behavior like fluid dynamics. So the Carnot efficiency is kind of like the Bernoulli equation or Reynolds number, and may have no analog at microscopic scales. Maybe something like:

https://en.wikipedia.org/wiki/Quantum_heat_engines_and_refri...