Lab 7: Thermodynamics — Reproducibility

Objective#

To simulate and validate thermodynamic behavior in triadic systems, including entropy modulation and harmonic energy transfer.

Required Tools#

• Python 3.10+
• NumPy
• SciPy
• Matplotlib or Plotly

Protocol#

1. Define Triadic Entropy Function#

python#

import numpy as np

def triadic_entropy(p, Rijk, kB=1.38e-23): return -kB * np.sum(p * np.log(p)) * Rijk

2. Simulate Harmonic Energy Transfer#

python#

from scipy.integrate import quad

def energy_transfer(dE_dt, omega, t0, t1): integrand = lambda t: dE_dt(t) * np.sin(omega * t) Q, _ = quad(integrand, t0, t1) return Q

3. Calculate Phase Transition Index#

python#

def phase_transition_index(delta_S, delta_T, gamma): return (delta_S / delta_T) * gamma

4. Triadic Heat Capacity#

python#

def triadic_heat_capacity(Q, delta_T, Rijk): return (Q / delta_T) * Rijk

###Validation Checklist

✅ Entropy values match expected triadic modulation#

✅ Energy transfer integrates correctly over harmonic cycles#

✅ Phase transition index reflects dimensional gain#

✅ Heat capacity scales with resonance#

Mythic Preface#

"In the furnace of dimensional resonance, entropy dances with harmonic time. This lab reveals the thermodynamic pulse of triadic cognition—where heat becomes memory and phase becomes myth."#