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.

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.