FirstOrderTransition
plain-language theorem explainer
FirstOrderTransition packages the observables of a discontinuous jump between two separated minima in the J-cost landscape, recording latent heat, volume change, and a hysteresis flag. Thermodynamic modelers working in Recognition Science cite the structure when classifying melting, boiling, or liquid-gas transitions from the bifurcation mechanism. It is introduced as a plain structure definition with three fields and no proof obligations.
Claim. A first-order transition is a triple consisting of latent heat $L : ℝ$, volume change $ΔV : ℝ$, and hysteresis indicator $h : Bool$, arising when the J-cost function possesses two distinct minima and the system jumps from one to the other as a control parameter varies.
background
Recognition Science treats phase transitions as bifurcations in the J-cost landscape. J-cost is the cost function induced by a multiplicative recognizer (MultiplicativeRecognizerL4.cost) or equivalently the J-cost of any recognition event (ObserverForcing.cost). Energy is identified with the reals (RSNativeUnits.Energy). Volume of a region is the cardinality of its vertex set (BrainHolography.volume). The module THERMO-006 sets the local goal of deriving all phase transitions from J-cost bifurcations, distinguishing first-order (discontinuous) from second-order (continuous but singular) cases.
proof idea
This declaration is a structure definition that directly assembles the three physical observables listed in the module comment. No lemmas or tactics are invoked; the fields latentHeat, volumeChange, and hysteresis simply record the energy difference, volume jump, and supercooling possibility that accompany a jump between distinct J-cost minima.
why it matters
The structure supplies the concrete data type for the first-order case inside the J-cost bifurcation program of THERMO-006 and the associated paper proposition on phase transitions as information-theoretic bifurcations. It distinguishes the discontinuous jump (two separated minima, nucleation across a barrier) from the second-order and critical-point siblings defined in the same module. It leaves open how the barrier height and nucleation rate are fixed by the underlying phi-ladder.
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