Thermodynamic Equivalence

Chapter 5: Thermodynamic Equivalence

Recasting Classical Entropy through Recursive Coherence

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5.1 Introduction

Though ITT arises from recursion-based field dynamics, it recovers key insights from classical thermodynamics—but through a new lens.

Rather than assuming entropy as a statistical aggregate, ITT roots entropy in information loss due to misaligned recursion.

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5.2 Mapping to Boltzmann’s Principle

Classical Form

ITT Reinterpretation

The “number of microstates” becomes the number of viable misaligned recursion configurations:

Then:

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5.3 Clausius Residue Equivalence

Classical Second Law

ITT Form

The “irreversible heat” becomes the irreversible drift residue:

Clausius	ITT
dQ (heat absorbed)	σθ dτ (drift accumulated)
T (temperature)	ℒ (lock—coherence)
dQ/T (entropy increment)	σθ dτ (unbinding increment)

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5.4 Temperature Mapping

ITT Temperature

Physical meaning:

• High drift, low lock → high T_ITT (hot)
• Low drift, high lock → low T_ITT (cold)
• At Planck-lock (ℒ = 1) → T_ITT = 0

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5.5 Time as Thermodynamic Progression

Interpretation: Time is the bookkeeping function for entropy progress.

Condition	Time Behavior
σθ = 0 (perfect lock)	Time halts
σθ large (high drift)	Time flows fast
σθ constant	Time flows uniformly

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5.6 The Second Law Reimagined

Classical: Entropy tends to increase in isolated systems.

ITT: Recursive glyphs tend to drift unless perfectly locked.

Key difference: No probability assumed. The Second Law emerges from the geometry of alignment tension.

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5.7 Summary: Translation Table

Classical Concept	Symbol	ITT Analog	Symbol
Entropy	S	Recursive entropy	Sθ
Temperature	T	Drift × (1−lock)	TITT
Heat	Q	Accumulated drift	∫σθ dτ
Microstates	W	Drift configurations	WITT
Boltzmann constant	kB	ITT entropy constant	kσ
Second Law	dS ≥ 0	Lock decay	dℒ/dn ≤ 0

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Next: Chapter 6 — Entropic Control of Delta

Back: Chapter 4 — Ceilings and Erasure