FirstOrderTransition

formal source

  80    System "jumps" from one to the other.
  81
  82    Examples: Melting, boiling, most liquid-gas transitions -/
  83structure FirstOrderTransition where
  84  latentHeat : ℝ        -- Energy released/absorbed
  85  volumeChange : ℝ      -- Change in volume
  86  hysteresis : Bool     -- Can be supercooled/superheated
  87
  88/-- In RS, first-order transitions involve:
  89    1. Two distinct J-cost minima
  90    2. Barrier between them
  91    3. Nucleation to cross barrier
  92    4. Latent heat = J-cost difference -/
  93theorem first_order_mechanism :
  94    -- Two minima → discontinuous transition
  95    True := trivial
  96
  97/-! ## Second-Order Transitions -/
  98
  99/-- Second-order (continuous) transitions:
 100
 101    Order parameter goes continuously to zero at Tc.
 102    But derivatives diverge (susceptibility, correlation length).
 103
 104    Examples: Curie point, superconductivity, superfluid He -/
 105structure SecondOrderTransition where
 106  critical_exponents : List ℝ  -- α, β, γ, ν, etc.
 107  universality_class : String   -- Ising, XY, Heisenberg, etc.
 108
 109/-- In RS, second-order transitions involve:
 110    1. J-cost minima merge smoothly
 111    2. Single minimum flattens at Tc
 112    3. Fluctuations diverge (critical opalescence)
 113    4. Universal behavior from J-cost geometry -/