`implications`

definition

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module: IndisputableMonolith.Thermodynamics.PartitionFunction
domain: Thermodynamics
line: 216 · github
papers citing: none yet

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IndisputableMonolith.Thermodynamics.PartitionFunction on GitHub at line 216.

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formal source

 213    2. **Response functions**: C_V, χ from derivatives of Z
 214    3. **Phase transitions**: Singularities in Z
 215    4. **Fluctuations**: ⟨(ΔE)²⟩ from Z -/
 216def implications : List String := [
 217  "Free energy F = -k_B T ln Z",
 218  "Entropy S = -∂F/∂T",
 219  "Heat capacity C = T ∂S/∂T",
 220  "Phase transitions from Z singularities"
 221]
 222
 223/-! ## Falsification Criteria -/
 224
 225/-- The derivation would be falsified if:
 226    1. Thermodynamic quantities don't follow from Z
 227    2. J-cost doesn't map to energy
 228    3. 8-tick doesn't give quantum statistics -/
 229structure PartitionFunctionFalsifier where
 230  thermo_from_z_fails : Prop
 231  jcost_not_energy : Prop
 232  eight_tick_not_quantum_stats : Prop
 233  falsified : thermo_from_z_fails ∨ jcost_not_energy ∨ eight_tick_not_quantum_stats → False
 234
 235end PartitionFunction
 236end Thermodynamics
 237end IndisputableMonolith

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