Conjugate Quanta of Action

Our core equation \[k_{B}T\ln(2)K(\mathrm{Q})\tau_0 \le A_L \le \pi \hbar\] sets a strict cap on how much algorithmic complexity a single quantum of action can contain: If one attempts to place all information for both position and momentum into one blob, they run into the fundamental limit imposed by the Planck constant, h. A single quantum blob in phase space represents an absolute minimum volume, leaving no room for precise conjugate values. To maintain a consistent physical description (which allows both position-space and momentum-space realities), the system must utilize two linked quanta of action---a conjugate pair.