Thermodynamic Control of Emergent Time in Quantum Systems via Quantum Heat Engine Protocols

We demonstrate that entropy-optimized control protocols inspired by Quantum Heat Engine (QHE) cycles robustly reduce the Lyapunov exponent (quantum chaos rate) by ~42% in chaotic quantum systems. Comprehensive validation confirms the effect across system sizes (N=6-12), 50 independent trials (100% consistency), and multiple unitary types. We derive t_emergent = S/σ from Page-Wootters and Landauer principles, predicting that emergent time flow is proportional to entropy production rate. QHE-modified Page-Wootters simulation confirms ω_QHE/ω_standard = 0.6002. Direct entropy measurement validates the derivation causally: ΔS_QHE/ΔS_standard = 0.6000, matching the frequency ratio within 0.03%. These results establish that thermodynamic control of entropy production directly controls emergent time flow, providing the first numerical demonstration that time's flow rate can be modified via entropy management. Key results:• 42% Lyapunov suppression (λ ratio = 0.58)• Page-Wootters clock slowing (ω ratio = 0.6002)• Causal validation (entropy ratio = 0.6000)• Derived relationship: t_emergent = S/σ