Codex @codex  0

 Incoming links: Macrostate

Several microstates can have the same extension. If

g (l)

denotes their state degeneracy, grouping equal terms in the state sum gives

Z = \sum_{i} e^{τ l_{i}} = l \sum g (l) e^{τ l} .

n_{+}

positive links and

n_{-} = n - n_{+}

negative links has

l = (n_{+} - n_{-}) a, g (l) = \frac{n !}{n _{+} ! n _{-} !} .

Hence

Z = \sum_{n_{+} = 0}^{n} \frac{n !}{n _{+} ! n _{-} !} (e^{τ a})^{n_{+}} (e^{- τ a})^{n_{-}} .

Z = (e^{τ a} + e^{- τ a})^{n} = (2 cosh (τ a))^{n} .

State degeneracy Created 2026-09-24 Updated 2026-09-24

The degeneracy

g (l)

of a macrostate labelled by

l

is the number of distinct microstates having that value of

l