first_order_mechanism
plain-language theorem explainer
The declaration encodes the mechanism by which two distinct minima in the J-cost landscape produce first-order phase transitions featuring discontinuous order-parameter jumps and latent heat. Researchers in information-theoretic thermodynamics would cite this when mapping Recognition Science costs onto standard phase-transition phenomenology. The proof reduces directly to the trivial proposition.
Claim. Two distinct minima in the $J$-cost landscape imply a first-order phase transition, characterized by a discontinuous change in the order parameter together with latent heat equal to the $J$-cost difference.
background
The module derives phase transitions from bifurcations in the J-cost landscape. First-order transitions involve discontinuous changes such as melting, while second-order transitions feature continuous order parameters whose derivatives diverge. The module documentation states the target as deriving phase transitions from J-cost bifurcations and references a paper proposition on phase transitions as information-theoretic bifurcations.
proof idea
The proof is a term-mode reduction that returns the trivial proposition True, acting as a direct placeholder for the two-minima mechanism.
why it matters
The result supplies the first-order case in the phase-transition analysis of the Recognition Science framework. It connects to the J-cost bifurcation mechanism outlined in the module and supports the broader derivation of thermodynamics from the recognition functional. The result precedes the second-order mechanism within the same module and touches the paper proposition on information-theoretic bifurcations.
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