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Aphoto-Carnot engine is aCarnot cycle engine in which the working medium is a photon inside a cavity with perfectly reflecting walls.Radiation is the working fluid, and the piston is driven byradiation pressure.

A quantum Carnot engine is one in which the atoms in the heat bath are given a small bit ofquantum coherence. The phase of the atomic coherence provides a new control parameter.^[1]

The deep physics behind thesecond law of thermodynamics is not violated; nevertheless, the quantum Carnot engine has certain features that are not possible in a classical engine.

The internal energy of the photo-Carnot engine is proportional to the volume (unlike the ideal-gas equivalent) as well as the 4th power of the temperature (seeStefan–Boltzmann law) using${\displaystyle a=\frac{4\sigma }{c}}$ :

${\displaystyle U=V\epsilon a{T}^4.}$

Theradiation pressure is only proportional to this 4th power of temperature but no other variables, meaning that for this photo-Carnot engine an isotherm is equivalent to an isobar:

${\displaystyle P=\frac{U}{3V}=\frac{\epsilon a{T}^4}{3}.}$

Using thefirst law of thermodynamics (${\displaystyle dU=dW+dQ}$) we can determine the work done through an adiabatic (${\displaystyle dQ=0}$) expansion by using the chain rule (${\displaystyle dU=\epsilon a{T}^{4}dV+4\epsilon aV{T}^{3}dT}$) and setting it equal to${\displaystyle d{W}_V=-PdV=-\frac{1}{3}\epsilon a{T}^{4}dV.}$

Combining these${\displaystyle d{W}_V=dU}$ gives us${\displaystyle -\frac{1}{3}TdV=VdT}$ which we can solve to find${\displaystyle T^{3}V=\text{const}}$, or equivalently${\displaystyle P{V}^{4/3}=\text{const}.}$

Since the photo-Carnot engine needs a quantum coherence in the gas which is lost during the process, the rebuild of coherency takes more energy than is produced with the machine.

The efficiency of this reversible engine including the coherency must at most be the Carnot efficiency, regardless of the mechanism and so${\displaystyle \eta \le \frac{T_H-T_C}{T_H}=1-\frac{T_C}{T_H}.}$

• Carnot heat engine
• Radiometer

• Marlan O. Scully; M. Suhail Zubairy; G. S. Agarwal; Herbert Walther (2003-02-07)."Extracting Work from a Single Heat Bath via Vanishing Quantum Coherence".Science.299 (5608):862–864.Bibcode:2003Sci...299..862S.doi:10.1126/science.1078955.PMID 12511655.S2CID 120884236.
• Zubairy, M. Suhail (2002). "The Photo-Carnot Cycle: The Preparation Energy for Atomic Coherence".Quantum Limits to the Second Law: First International Conference on Quantum Limits to the Second Law. AIP Conference Proceedings. Vol. 643. pp. 92–97.Bibcode:2002AIPC..643...92Z.doi:10.1063/1.1523787.

• Hot air engines
• Thermodynamic cycles

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