non-gibbs-quantum-stats

# Non-Gibbs Quantum Statistics ## Problem Redfield quantum master equation with secular approximation thermalizes to Gibbs state. But non-secular terms can drive the system into a non-Gibbs steady state. ## Key Mechanism For two strongly interacting quantum oscillators with independent baths at equal temperature: - **Non-secular terms** → excitation flux driven by bath-induced coherences - **Unequal damping** → steady state occupation deviates from Boltzmann distribution - **Nearly-degenerate levels** → coherences between oscillator levels cause non-thermal occupation ## Mathematical Framework ### Redfield Equation ``` dρ/dt = -i[H, ρ] + R(ρ) ``` where R(ρ) contains secular and non-secular contributions. ### Secular Approximation - Preserves positivity of reduced density operator - Thermalizes to Gibbs state: ρ ∝ exp(-βH) ### Non-Secular Effects - Drive system to non-Gibbs state - Bath-induced coherences between nearly-degenerate levels - Excitation flux depends on relative bath couplings ## Conditions for Gibbs Recovery 1. Equal damping by baths 2. Large level spacing (no near-degeneracy) 3. Weak system-bath coupling 4. Secular approximation valid ## Applications - Open quantum system dynamics - Quantum thermodynamics - Quantum statistical mechanics - Quantum heat engines and refrigerators - Non-equilibrium quantum states ## Trigger Keywords quantum statistics, Gibbs state, Redfield equation, non-secular, bath coherence, thermalization, open quantum systems, quantum thermodynamics, Boltzmann distribution ## Reference - arXiv:2606.00239: "Bath-induced deviations from Gibbs statistics for strongly interacting oscillators" (Recabal et al., 2026)