tags: - colorclass/a thermodynamic theory of statistical learning ---Let’s derive information conductivity from information theoretic principles:
1. Fick’s First Law analog for information flow: J = -σ∇I
where: - J: information current - σ: information conductivity - ∇I: information gradient
2. Define conductivity in terms of channel capacity: σ = C/η
where: - C: channel capacity (bits/sample) - η: learning rate (as resistance analog)
3. Channel capacity from noise model: C = (1/2)log(1 + SNR)
where SNR is signal-to-noise ratio for dataset.
4. Therefore information conductivity: σ = (1/2η)log(1 + Q/N)
where: - Q: dataset quality metric - N: noise/uncertainty in dataset
This gives theoretical basis for earlier simulation’s conductivity parameter. Want me to expand on any part?