remark 31.92 Entropy selects the physical branch

Rests on

• depends_on theorem 31.91 Rankine–Hugoniot jump conditions ¶
  • depends_on theorem 31.12 Conservation of mass ¶
    • depends_on lemma 31.11 Transport theorem for a material volume ¶
      • depends_on definition 31.4 Material derivative ¶
        • depends_on equation 7.124 eq:ana-nabla-gradient ¶
        • depends_on proposition 7.104 Chain rule in several variables ¶
        • proves proof ch:14-fluid-dynamics@proof-1 ¶
      • depends_on theorem 7.133 Gauss ¶
        • depends_on definition 7.127 Simple regions ¶
        • depends_on remark 7.128 What the derivations below take as given ¶
        • depends_on theorem 7.43 Fundamental theorem of calculus, II ¶
        • proves proof ch:05-real-analysis@proof-79 ¶
      • proves proof ch:14-fluid-dynamics@proof-4 ¶
    • proves proof ch:14-fluid-dynamics@proof-5 ¶
  • depends_on theorem 31.22 Euler's equations of motion ¶
    • depends_on definition 31.21 Ideal fluid ¶
      • depends_on definition 31.1 Fluid ¶
        • depends_on theorem 30.18 Cauchy: the stress tensor exists ¶
    • depends_on lemma 31.11 Transport theorem for a material volume ¶ ↺
    • depends_on theorem 30.21 Cauchy's equation of motion ¶
      • depends_on theorem 7.133 Gauss ¶ ↺
      • depends_on theorem 30.18 Cauchy: the stress tensor exists ¶ ↺
      • proves proof ch:13-continuum-elasticity@proof-9 ¶
    • proves proof ch:14-fluid-dynamics@proof-11 ¶
  • proves proof ch:14-fluid-dynamics@proof-45 ¶

Supports

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