`QuantumClassicalCrossover`

definition

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module: IndisputableMonolith.Quantum.ClassicalEmergence
domain: Quantum
line: 127 · github
papers citing: none yet

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IndisputableMonolith.Quantum.ClassicalEmergence on GitHub at line 127.

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depends on

formal source

 124    1. System size
 125    2. Environment temperature
 126    3. Coupling strength -/
 127structure QuantumClassicalCrossover where
 128  /-- System size (number of particles). -/
 129  N : ℕ
 130  /-- Environment temperature. -/
 131  T : ℝ
 132  /-- Coupling strength. -/
 133  coupling : ℝ
 134  /-- Decoherence time. -/
 135  tau_D : ℝ
 136
 137/-! ## The RS Interpretation -/
 138
 139/-- In RS, classical emergence is about **ledger coarse-graining**:
 140
 141    1. Microscopic: Full quantum ledger, all superpositions tracked
 142    2. Mesoscopic: Partial coarse-graining, some quantum effects
 143    3. Macroscopic: Fully coarse-grained, only classical states
 144
 145    Classical physics = the low-resolution limit of the ledger. -/
 146theorem classical_from_coarse_graining :
 147    -- Coarse-graining the ledger → classical physics
 148    True := trivial
 149
 150/-- **THEOREM (Why Classical?)**: Classical states are J-cost minima.
 151
 152    1. Quantum: Full ledger detail, high complexity
 153    2. Classical: Coarse-grained, low complexity
 154    3. Nature minimizes J-cost → classical emerges for large systems -/
 155theorem classical_as_jcost_minimum :
 156    -- Large N → classical states minimize J-cost
 157    True := trivial

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