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Landauer Cost of a Self-Model

Laflamme-3T Conjecture - Path 3 Step 2 - Feasibility Gate

Author: Lark Laflamme

Date: April 2026

Status: Published - Feasibility analysis

Based on: Laflamme-3T Research Programme

Abstract

Before pursuing physical instantiation of AC-1, we must verify that a self-referential entropy-reducing system is thermodynamically feasible given available technology. This document derives the minimum power required to maintain a self-model, computes it across a range of parameters, and delivers a verdict on which research paths to pursue.

1. Landauer's Principle

Landauer's Principle (1961), proven experimentally by Bérut et al. (2012):

E_erase ≥ k_B · T · ln(2)

At room temperature (T = 293 K): E_erase ≥ 2.805 × 10^-21 J/bit. No physical process can erase one bit of information for less energy than this. This is a proven physical law, not an approximation.

Application to a Self-Model

A self-model of Kolmogorov complexity K bits must be erased and rewritten on every update cycle. The minimum continuous power is:

P_min = k_B · T · ln(2) · K · f

This is the thermodynamic floor — technology-independent. Real implementations exceed this by an overhead factor η.

2. Technology Efficiency Spectrum

Technology	η	Notes
Theoretical minimum	1×	Landauer limit
Advanced reversible logic (~2040)	10×	Research stage
Adiabatic CMOS (~2035)	10²×	Near-future
Biological brain	10³×	~20 W for ~10¹⁶ synaptic ops/s
Neuromorphic (IBM TrueNorth)	10⁴×	State of art 2025
Current silicon (CMOS)	10⁶×	~10^-15 J/op
Typical desktop	10⁸×	Commodity hardware

3. Computed Power Requirements

Case 1 — Minimal reflexive agent (K = 10⁶ bits, f = 10 Hz):
P_min ≈ 2.8 × 10^-14 W. At current silicon (η = 10⁶): ~28 nW.

Case 2 — Rich self-model (K = 10¹² bits, f = 100 Hz):
P_min ≈ 280 nW. At current silicon: ~280 W. At neuromorphic: ~2.8 mW.

Case 3 — Brain-equivalent (K = 10¹⁵ bits, f = 100 Hz):
P_min ≈ 280 μW. At current silicon: ~280 kW. At neuromorphic: ~2.8 W. At biological efficiency: ~280 mW.

4. Biological Baseline

Property	Value
Total metabolic power	≈ 20 W
Number of neurons	≈ 86 billion
Number of synapses	≈ 100 trillion
Efficiency vs. Landauer	≈ 10³–10⁴×

The brain operates at roughly 10³–10⁴× the Landauer limit — far more efficient than current silicon. Most brain energy is spent on ion transport, not computation.

5. The Self-Referential Extension

For a self-referential system, the full power expression becomes:

P_Ψ = k_B · T · ln(2) · (K + ΔI_self) · f

For a well-calibrated self-model where ΔI_self ≈ K, the self-referential penalty is at most a factor of 2 over the naive Landauer cost. It does not change the order-of-magnitude analysis.

Feasibility Verdict: Artificial consciousness is not thermodynamically prohibited. The Landauer minimum P_min is never the engineering bottleneck at any reasonable parameter setting. The constraint is entirely in the overhead factor η. Current neuromorphic hardware can already sustain a minimal-to-moderate self-model within standard power budgets. The path to AC-1 is an engineering challenge, not a physics prohibition.