PhysicsLogic / Onsager 1931

Onsager's Fixed-Temperature Variation

Inspect the physical force, the varied functional, and the restrictions that change an extremum claim.

Definitions and assumptions

Scope and physical limitations

This view covers the selected heat-flow variational argument in Part I, sections 5-6. Reciprocity, constitutive physics, spatial integral representations, and Green's identity have explicit roles. It is not a derivation of microscopic reversibility, a universal maximum-entropy-production principle, or a fitted continuum crystal.

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Examples and distinctions

Constructed examples of this model; each answer includes the Lean statement.

Exact root statement

∀ {Flow : Type u} [inst : AddCommGroup Flow] [inst_1 : Module ℝ Flow] (data : DissipationFunctional.Data Flow),
  data.ReciprocalAt →
    data.StrictDissipationAt →
      ∀ (physical : Flow), physical ≠ 0 → data.ConstitutiveAt physical → data.NonvacuousDissipationMaximumAt physical
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Notes and questions

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Definitions, structures, and assumptions

Structures, classes, and inductive alternatives

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Checked statements: parameters, hypotheses, and interpretation

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Constructors, projections, and other meaning dependencies

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External mathematical declarations

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