IndisputableMonolith.Thermodynamics

   1import IndisputableMonolith.Thermodynamics.RecognitionThermodynamics
   2import IndisputableMonolith.Thermodynamics.MaxEntFromCost
   3import IndisputableMonolith.Thermodynamics.FreeEnergyMonotone
   4import IndisputableMonolith.Thermodynamics.ErrorCorrection
   5import IndisputableMonolith.Thermodynamics.PhaseTransitions
   6import IndisputableMonolith.Thermodynamics.MemoryLedger
   7
   8/-!
   9# Recognition Thermodynamics
  10
  11This module develops the statistical mechanics of Recognition Science (RS).
  12
  13## Overview
  14
  15Recognition Science has established a "T=0" foundation where reality is defined by
  16the absolute minimization of a universal cost functional J(x) = ½(x + 1/x) - 1.
  17This module extends RS to finite Recognition Temperature (TR), enabling:
  18
  191. **Noise and Fluctuations**: Understanding "almost-stable" states
  202. **Learning and Exploration**: The exploration-exploitation tradeoff
  213. **Arrow of Time**: Global relaxation toward low free energy
  224. **Error Correction**: Fault tolerance as the origin of physical law stability
  235. **Memory Dynamics**: Retention vs. free-energy decay
  24
  25## Submodules
  26
  27- `RecognitionThermodynamics`: Core definitions (TR, β, Gibbs measure, SR, FR)
  28- `MaxEntFromCost`: Gibbs minimizes free energy, maximizes entropy for fixed cost
  29- `FreeEnergyMonotone`: Second Law of Recognition (dFR/dt ≤ 0)
  30- `ErrorCorrection`: Error correction viewpoint, fault tolerance thresholds
  31- `PhaseTransitions`: Critical phenomena, coherence threshold C=1
  32- `MemoryLedger`: Memory as thermodynamic system (Priority #6 from RS_UNDISCOVERED_TERRITORIES)
  33
  34## Key Concepts
  35
  36### Recognition Temperature (TR)
  37Parameterizes the strictness of J-minimization:
  38- TR = 0: Deterministic RS (only J=0 states exist)
  39- TR = T_φ = ln(φ): Critical point (C=1 coherence threshold)
  40- TR → ∞: Maximum disorder (uniform distribution)
  41
  42### Recognition Free Energy (FR)
  43The fundamental variational quantity:
  44  FR(p) := E_p[J] - TR × SR(p)
  45
  46The Gibbs measure minimizes FR:
  47  p_G(x) ∝ exp(-J(x)/TR)
  48
  49### Arrow of Time
  50Time flows in the direction of decreasing FR:
  51  dFR/dt ≤ 0
  52
  53This unifies:
  54- Thermodynamic arrow (entropy increase)
  55- Cosmological arrow (universe expansion toward equilibrium)
  56- Psychological arrow (learning, adaptation)
  57
  58## References
  59
  60- RS_UNDISCOVERED_TERRITORIES.md
  61- Recognition-Science-Full-Theory.txt
  62- Statistical Mechanics of Recognition (paper draft)
  63-/
  64