Quantum Thermodynamics — Two-Level Quantum Otto Engine

A qubit as working fluid: energy levels split by field ω. Four strokes — quantum adiabatic compression/expansion + hot/cold isochoric heat exchange

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Quantum Otto cycle (two-level system): Stroke 1 — quantum adiabatic compression: ω₁→ω₂=r·ω₁, populations frozen. Stroke 2 — hot isochore: system thermalizes to T_H at ω₂ (heat absorbed Q_H). Stroke 3 — quantum adiabatic expansion: ω₂→ω₁, populations frozen. Stroke 4 — cold isochore: system thermalizes to T_C at ω₁ (heat rejected Q_C). Otto efficiency η_Otto = 1 − ω₁/ω₂ = 1 − 1/r, always ≤ Carnot η_C = 1−T_C/T_H. Population of excited state: p_e = 1/(e^(ω/T)+1) (Fermi–Dirac for spin-½).