Manuscript En03-A@1 · En03-A.tex · definition · 5398614e

Definition: Scheduled matter dynamics

Kinematics and causal cuts on a prescribed schedule › Scheduled blocks · lines 604–627

En03-A@1#def:schedule, En03-A@1#eq:scheduled-dynamics

Let $(X, d)$ be a finite metric space with site spaces $H_{x}$ , and write

H_{X} = x \in X ⨂ H_{x}, A (Y) = L (x \in Y ⨂ H_{x}) \otimes I_{X ∖ Y} .

For $a, τ > 0$ , let $B_{t}$ be a partition of $X$ at tick $t = 1, \dots, T$ , with

diam_{d} B \leq R_{upd} a .

The dynamics is

Φ_{t} = B \in B_{t} ⨂ Φ_{t, B}, c_{sched} = \frac{R _{upd} a}{τ},

where each block map is a channel on its reserved site interface.

Displayed formulas in this passage

En03-A@1#eq:scheduled-dynamics · line 620
$Φ_{t} = B \in B_{t} ⨂ Φ_{t, B}, c_{sched} = \frac{R _{upd} a}{τ},$
unlabeled · line 608
$H_{X} = x \in X ⨂ H_{x}, A (Y) = L (x \in Y ⨂ H_{x}) \otimes I_{X ∖ Y} .$
unlabeled · line 616
$diam_{d} B \leq R_{upd} a .$