J ↔ q
Tier II — Similarity EMPIRICAL
- Object
- heat_conducting_medium
- Property
- HeatFluxDensity
- Context
- near_equilibrium
Sieve rationale
Structural equation-level identity (sign=+1): the canonical forms of EQ-FICK-DIFFUSION and EQ-FOURIER-HEAT are syntactically equal under rename, and J maps to q under the discovered bijection
Physical constraint filter
Both variables are bond-graph flows but pint dimensions differ ([substance] / [length] ** 2 / [time] vs [mass] / [time] ** 3); accepted as a STRUCTURAL flow-analogy (e.g., force ↔ voltage: both occupy the effort slot in their respective bond graphs but are not dimensionally equal). Any downstream composite that needs a numerical identity must supply a transducer coefficient.
Both equations are linear transport laws; for a single-variable coupling the Onsager matrix is 1x1 and symmetric by construction.
Energy conservation check is narrowly targeted at the Newton+Hooke → SHO composite in Medium m2; other composites require the Phase 7 Lyapunov/Noether machinery (not yet built).
Emergent properties
AI review board
1 REJECT vote(s); the coupling is demoted to conjectural per §12.2.
This is a well-known and physically legitimate structural analogy between Fick's law of diffusion (J = -D ∇C) and Fourier's law of heat conduction (q = -k ∇T). Both are linear, first-order transport laws of identical mathematical form, and the coupling correctly identifies J (molar flux) and q (heat flux density) as the analogous flow variables in their respective bond-graph representations. The semantic descriptors are honest: they do not claim dimensional equality but rather structural correspondence, and the Tellegen pairing check correctly notes that dimensions differ while accepting the analogy at the structural level. The Onsager reciprocity check is trivially satisfied for single-flux laws. The transfer function is listed as 'identity,' which is appropriate for a structural (syntactic) mapping rather than a numerical one, and the sieve reason explicitly states this is a rename-level bijection. The Buckingham pi groups are the standard dimensionless forms of each law. No spurious emergent properties are claimed. The only caveat — that any downstream numerical coupling must supply a transducer coefficient — is properly noted in the evidence. This is a textbook example of a valid cross-domain transport analogy.
While Fick’s and Fourier’s laws are structurally isomorphic, J (molar flux) and q (heat-flux density) are distinct quantities with incompatible dimensions; equating them via an identity transfer function is not physically meaningful. The filter’s flow–flow pass only supports a structural analogy, not numerical identity, and a valid cross-domain link would require an explicit, unit-bearing transduction (e.g., enthalpy-per-mole relating convected heat to mass flux, or named Soret/Dufour cross-coefficients). The reported π-groups are tautologies of the base laws, not genuine emergent properties. Hence the proposed identity coupling is not acceptable for the ledger.
The proposed coupling represents a classic, physically sound analogy between heat and mass transport, as both are governed by structurally identical linear flux-gradient laws. The semantic descriptors are accurate, correctly identifying the distinct physical nature of molar flux and heat flux density. The physical constraint filter's assessment is robust, appropriately treating the coupling as a structural analogy (akin to a bond-graph flow-flow pairing) and correctly verifying the Onsager symmetry. The emergent property analysis is non-artefactual, further confirming the validity of this fundamental cross-domain mapping for inclusion in the discovery ledger.