KDA Physics: Thermodynamic Energy Recovery# KDA Physics

Authors: Research Stack Team Date: April 2026 Domain: TTM Layer A (Compression/Routing) + Physics OTOM Version: 2.2

References: See 00_Master_References.md for complete source mapping

Abstract

The KDA (Kinetic-Dynamic-Atomic) Physics framework models shock physics and energy recovery for sovereign energy systems. It establishes the theoretical foundations for Maxwell's Demon efficiency in compression systems. The physics framework is now extended with geometric structure folding (Torus-Menger-Horn) for energy flow optimization and Mass Number gates for thermodynamic admissibility.

1. Introduction

KDA Physics addresses the thermodynamic limits of computational compression, treating information processing as a physical process subject to Landauer's principle.

2. Shock Physics

2.1 Pressure Piling (Sequential Shock Amplification)

P(i) = P_0 \cdot \chi^i \quad (\chi \approx 1.63)

Sequential shock amplification through the KDA stack.

2.2 Hugoniot Temperature

T_{\text{peak}} = T_0 \cdot \left(\frac{P_{\text{peak}}}{P_0}\right)^{0.65}

Non-isentropic shock heating relationship.

2.3 Pressure Ionization

\alpha(P) = 1 - e^{-k(P - P_{\text{MIT}})}

Insulator-to-metal transition probability.

3. Energy Recovery

3.1 Net Efficiency

\eta_{\text{net}} = \frac{W_{\text{rec}} - W_{\text{erasure}}}{W_{\text{in}}}

3.2 Q-Factor (Global Energy Balance)

Q = \frac{E_{\text{flash}} + E_{\text{enthalpy}} + E_{\text{recovered}} - W_{\text{demon}}}{E_{\text{work}} + E_{\text{loss}}} > 1.0

4. Landauer Bound

W_{\text{erasure}} \geq k_B T \ln(2)

Per bit erasure at T_{\text{peak}} \approx 13,446 K.

5. Implementation

Location:

core/intrinsic/formalisms/9_KDA_Equation_Manifest.md
11_KDA_Material_Manifest.md
4_KDA_Plasma_Hysteresis_Device.md

Lean 4 Modules:

ThermodynamicSort.lean
LandauerCompression.lean

6. References

Landauer, R. (1961). Irreversibility and heat generation in computing.
Bennett, C.H. (1982). Thermodynamics of computation.
Research Stack, OTOM Ontology v2.2.

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