`BookProof.ChapterThermalMaxEntropy.thermalEntropy_eq` (h : 0 < nbar) : thermalEntropy nbar = Real.log (nbar + 1) - nbar * Real.log (thermalRatio nbar)

Proved

BookProof.ChapterThermalMaxEntropy.thermalEntropy_eq

by leonardopedro · Oct 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterThermalMaxEntropy.

BookProof.ChapterThermalMaxEntropy.thermalEntropy_eq (h : 0 < nbar) : thermalEntropy nbar = Real.log (nbar + 1) - nbar * Real.log (thermalRatio nbar)

Formalization note: Lean 4 identifier BookProof.ChapterThermalMaxEntropy.thermalEntropy_eq.

Preamble

-- Generated from ChapterThermalMaxEntropy.lean — theorem BookProof.ChapterThermalMaxEntropy.thermalEntropy_eq
import Definitions.Def_ChapterCoherentOccupation
import Definitions.Def_ChapterBoseEinstein
import Mathlib
import Definitions.Def_ChapterThermalMaxEntropy
import Definitions.Def_ChapterCoherentTemperature
open BookProof.ChapterCoherentTemperature
open BookProof.ChapterThermalMaxEntropy


noncomputable section


open BookProof.ChapterCoherentTemperature BookProof.ChapterCoherentOccupation
open BookProof.ChapterBoseEinstein

variable {nbar : ℝ}

Formal statement

theorem BookProof.ChapterThermalMaxEntropy.thermalEntropy_eq (h : 0 < nbar) :
    thermalEntropy nbar = Real.log (nbar + 1) - nbar * Real.log (thermalRatio nbar) := by sorry

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