| … | … | @@ -584,7 +584,37 @@ The sum ranges over all possible connected graphs over the words in the |
| 584 | 584 | \end_layout |
| 585 | 585 | |
| 586 | 586 | \begin_layout Standard |
| 587 | | Here, we arrive at the next stumbling block |
| 587 | Here, we arrive at the next stumbling block. |
| 588 | Is it correct to call |
| 589 | \begin_inset Formula $h\left(G\right)$ |
| 590 | \end_inset |
| 591 | |
| 592 | the energy, or is it something else? The above has the classic form of |
| 593 | a superposition. |
| 594 | If we interpret a single graph to be a |
| 595 | \begin_inset Quotes eld |
| 596 | \end_inset |
| 597 | |
| 598 | state |
| 599 | \begin_inset Quotes erd |
| 600 | \end_inset |
| 601 | |
| 602 | , then the above is a superposition of states, and |
| 603 | \begin_inset Formula $H\left(S\right)$ |
| 604 | \end_inset |
| 605 | |
| 606 | should be interpreted as the partition function, and not the energy. |
| 607 | For partition functions, the appropriate notation would be a Boltzmann |
| 608 | sum: |
| 609 | \begin_inset Formula |
| 610 | \[ |
| 611 | Z_{\beta}=\sum_{G\in\mathcal{G}}e^{-\beta h\left(G\right)} |
| 612 | \] |
| 613 | |
| 614 | \end_inset |
| 615 | |
| 616 | So, which is it? I'm confused, here. |
| 617 | |
| 588 | 618 | \end_layout |
| 589 | 619 | |
| 590 | 620 | \begin_layout Section* |