The Thermodynamics of Computation: Landauer's Limit, Entropy, and Mind

Information is not an abstract mathematical ideal—it is physical. Rolf Landauer proved in 1961 that erasing one bit of physical information dissipates a fundamental minimum amount of heat.

Landauer's Thermodynamic Bound

The minimum heat dissipation $Q$ required to erase one classical bit at temperature $T$ is:

Where: - $k_B = 1.380649 \times 10^{-23} \text{ J/K}$ (Boltzmann constant) - At room temperature $T = 300\text{ K}$, $\Delta Q \approx 2.87 \times 10^{-21} \text{ Joules}$.

Shannon vs. Gibbs Entropy

The profound mathematical equivalence uniting statistical mechanics and digital information theory:

Philosophical Implications for Cognitive Architecture

If logical irreversibility mandates thermodynamic dissipation, physical minds operating at finite energy budgets must optimize for predictive coding and compression. Consciousness may be the thermodynamic steady-state of an active inference engine minimizing variational free energy: