# Regimes — Thermodynamics  
### TriadicFrameworks /docs/theories/thermodynamics/regimes.md

Thermodynamics is the **R1 constraint‑first substrate grammar** of the RTT
stack. It defines how temperature, entropy, free energy, and flows behave
under different coherence conditions and scales. Thermodynamics is not a
mechanical theory — it is a **constraint geometry**.

This file defines Thermodynamics across RTT regimes R1 → R4.

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# R1 — Constraint Substrate Regime  
### (Thermodynamics fully valid • substrate grammar active)

In R1:

- temperature acts as a **substrate force**  
- entropy defines **regime boundaries**  
- free energy defines **coherence direction**  
- flows follow **gradients**  
- equilibrium is a **fixed‑point structure**  
- no microstate counting required  
- no field‑level corrections  

This is **canonical Thermodynamics**.

**Interpretation:**  
Thermodynamics is fully valid and self‑contained.

---

# R2 — Statistical Mechanics Regime  
### (Microstate structure emerges • ensembles refine thermodynamics)

In R2:

- microstates become explicit  
- partition functions define structure  
- ensembles (canonical, grand canonical) appear  
- entropy gains statistical interpretation  
- fluctuations become meaningful  

Thermodynamics survives as:

- the **macro‑limit**  
- the **constraint envelope**  
- the **coarse‑grained grammar**  

**Interpretation:**  
Thermodynamics is embedded inside Statistical Mechanics.

---

# R3 — Field‑Theoretic Regime  
### (Thermodynamics embedded in QFT • phase transitions become field‑level)

In R3:

- free energy becomes field‑dependent  
- renormalization affects thermodynamic quantities  
- phase transitions become field‑theoretic  
- vacuum structure influences equilibrium  
- entropy includes field‑mode contributions  

Thermodynamics cannot describe:

- running couplings  
- field‑level critical behavior  
- vacuum‑driven transitions  

**Interpretation:**  
Thermodynamics is no longer complete; QFT dominates.

---

# R4 — Cosmological Regime  
### (Horizon thermodynamics • geometric temperature • cosmological entropy)

In R4:

- horizon entropy dominates  
- temperature becomes geometric (e.g., Unruh, Hawking)  
- equilibrium becomes cosmological  
- free energy loses local meaning  
- entropy includes horizon‑scale contributions  

Thermodynamics cannot describe:

- horizon‑scale coherence  
- cosmological vacuum structure  
- gravitational entropy sources  

**Interpretation:**  
Thermodynamics requires cosmology or quantum gravity.

---

# Summary

Thermodynamics behaves as:

- **R1:** constraint‑first substrate grammar (fully valid)  
- **R2:** statistical refinement (microstate‑embedded)  
- **R3:** field‑theoretic embedding (QFT‑dominated)  
- **R4:** cosmological embedding (horizon‑dominated)  

Thermodynamics is the **constraint substrate** from which Statistical
Mechanics emerges and into which QFT and Cosmology embed their
large‑scale behavior.