Thermodynamic laws and transformations for single or few quantum systems. Foundational: Jarzynski 1997 equality ⟨e^(-βW)⟩ = e^(-βΔF) — free-energy differences recoverable from non-equilibrium work distributions; Crooks 1999 fluctuation…
quantum-thermodynamics
Jarzynski 1997: ⟨exp(-βW)⟩ = exp(-βΔF) — non-equilibrium avg recovers equilibrium ΔF
Jarzynski 1997 equality (PRL 78:2690). For a system initially in thermal equilibrium at temperature T, driven arbitrarily far from…
Crooks 1999: P_F(W)/P_R(-W) = exp(β(W - ΔF)) — forward/reverse work-PDF ratio
Crooks 1999 fluctuation theorem (PRE 60:2721) — stronger statement than Jarzynski. For a system driven by a time-dependent protocol λ(t)…
Quantum Otto cycle: 2 adiabatic + 2 isochoric — frequency-change expansion/compression
Quan-Liu-Sun 2007 quantum Otto cycle (PRE 76:031105): four-stroke thermodynamic cycle on a quantum working substance (e.g. harmonic…
Gaussian-work limit: ⟨W⟩ = ΔF + β σ_W²/2 (cumulant identity)
Gaussian-work limit of the Jarzynski equality. When the work distribution P(W) is Gaussian with mean μ and variance σ² (near-equilibrium…
Crooks ratio: [P_F(W)/P_R(-W)]·exp(-β(W-ΔF)) = 1 — identity along entire W axis
Restatement of the Crooks fluctuation theorem as an identity along the entire work axis: whenever both P_F and P_R are non-zero,…
Otto efficiency: η = 1 − ω_c/ω_h for harmonic-oscillator quantum substrate
For the quantum Otto cycle on a harmonic-oscillator substrate with trap frequencies ω_c < ω_h, the efficiency is η_Otto = 1 − ω_c/ω_h —…