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 —…
Landauer erasure: Delta-Q >= k_B*T*log(2) per erased bit via Shannon-McMillan-Breiman AEP
Landauer erasure bound and Shannon-McMillan-Breiman AEP. Setup: a one-bit memory register in a thermal reservoir of temperature T; erasing…
Jarzynski-via-Jensen second-law corollary: <W> >= dF (Jensen on convex exp(-x))
Jarzynski equality combined with Jensen's inequality gives the second-law corollary. Setup: a classical or quantum system driven out of…
Thermodynamic uncertainty relation (TUR): Var(J)/<J>^2 >= 2*k_B/<Sigma> via large-deviations
Thermodynamic uncertainty relation (Barato-Seifert 2015, Gingrich-Horowitz-Barato-England 2016). Setup: a non-equilibrium steady-state…
Landauer bound Q_min = k_B*T*log(2); at T = 300 K, Q_min ~ 2.87e-21 J/bit
Landauer bound exact value. From framework F7 (SMB-AEP reduction to single-bit), the minimum heat dissipated per logical bit erasure is…
Jarzynski-Jensen: exp(-beta*<W>) <= <exp(-beta*W)> = exp(-beta*dF); hence <W> >= dF
Jarzynski-Jensen second-law corollary. From framework F8, combine Jensen's convexity inequality E[exp(-X)] >= exp(-E[X]) with Jarzynski's…
TUR saturation at minimal dissipation: Var(J) = 2*k_B*<J>^2/<Sigma>; ratio = 2*k_B/<Sigma>
TUR saturation regime: fractional-uncertainty floor. From framework F9 (TUR), the equality Var(J)/<J>^2 = 2*k_B/<Sigma> is saturated by…
Jarzynski (quantum)
C Jarzynski 1997 quantum Jarzynski equality + 2-point measurement scheme; modern characteristic-function approach Talkner-Hanggi 2007.
Crooks (1999)
G Crooks 1999 quantum-extension; ratio of forward/reverse work distributions = exp((W-Delta-A)/kT); experimental Naghiloo 2020.
Landauer principle (1961)
R Landauer 1961: erasing 1 bit dissipates kT ln 2; modern Berut 2012 + Yan 2018 single-bit-erasure experimental verification.
Quantum Otto cycle
Quan-Liu 2007 quantum Otto-engine; isolated + thermalization strokes; modern superconducting-circuit experimental demonstrations.
Third law (quantum)
Levy-Kosloff 2012 quantum third-law unattainability; modern equilibration-time scaling with energy-gap; basis of quantum-refrigeration…
ETH + thermalization
Deutsch 1991 + Srednicki 1994 ETH; modern Eisert 2015 'Quantum Many-Body Systems Out of Equilibrium' review; closed-quantum-system…
Scovil-Schulz-DuBois (1959)
H Scovil-E Schulz-DuBois 1959 first quantum-heat-engine 3-level maser; modern modern foundational text + quantum-Otto + Carnot bounds.
Kosloff (1984)
R Kosloff 1984 quantum-thermo formal; modern modern foundational text + Kosloff-Levy 2014 review + endo-reversible quantum thermo.
Jarzynski (1997)
C Jarzynski 1997 free-energy from non-eq work; modern modern foundational text + Crooks 1999 + experimental-confirmation Liphardt 2002.
Crooks fluctuation (1999)
G Crooks 1999 fluctuation-theorem; modern modern foundational text + 2nd-law-fluctuations + Hummer-Szabo 2001 reconstruction.
Landauer bound (1961)
R Landauer 1961 erasure W ≥ kT ln 2; modern modern foundational text + Bennett 1982 reversible + 2012 measurement-Landauer test.
Maxwell demon (Szilárd 1929)
L Szilárd 1929 single-bit-engine + Bennett 1987; modern modern foundational text + experimental Toyabe 2010 + Pekola 2014 single-electron.