ledgerProperties

formal source

 115    2. **Energy assignment**: J-cost determines "energy"
 116    3. **Degeneracy**: Multiple entries with same cost
 117    4. **Conservation**: Total ledger balance is conserved -/
 118def ledgerProperties : List String := [
 119  "Discrete microstates from ledger entries",
 120  "J-cost plays role of energy",
 121  "Degeneracy from ledger symmetries",
 122  "Conservation laws from ledger balance"
 123]
 124
 125/-! ## The J-Cost Connection -/
 126
 127/-- The fundamental connection:
 128
 129    E_state ↔ J_cost(ledger_entry)
 130
 131    A low J-cost state is "low energy" and favored.
 132    A high J-cost state is "high energy" and suppressed. -/
 133noncomputable def energyFromJCost (x : ℝ) : ℝ := Jcost x
 134
 135/-- The temperature sets the scale for J-cost fluctuations.
 136
 137    - Low T: Only lowest J-cost states occupied
 138    - High T: All states approximately equally occupied
 139    - T → ∞: Maximum entropy (all states equally likely) -/
 140theorem temperature_controls_fluctuations :
 141    True := trivial
 142
 143/-! ## Special Cases -/
 144
 145/-- Two-level system (simplest example).
 146
 147    E₀ = 0 (ground state)
 148    E₁ = ε (excited state)