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zexxa

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**Question**Form the canoncial partition using the following conditions:

- 2 N-particles long strands can join each other at the
*i*-th particle to form a double helix chain. - Otherwise, the
*i*-th particle of each strand can also be left unattached, leaving the chain "open" - An "open" link gives the strand ##\epsilon## amount of energy where ##\epsilon > 0##
- A "closed" link gives the strand no energy

- For ##m < N##, the strand must be "open" for ##i \leq m## and "closed" for ##m < i \leq N##
- Note that ##m \neq N##
- Each particle are independent of each other and they weakly interact

Attempt

Attempt

I treated the energy states at ##i /leq m## and ## i > m## as a simple one energy state i.e.

## E = \sum_i ^N n_i \epsilon , {n_i} = \begin{cases} 1, & \text{if $i \leq m$}.\\

0, & \text{otherwise} \end{cases}##

Therefore,

##Z(\beta , V , N) = \{ exp[ - \beta \epsilon ] \} ^m \{ exp[ 0 ]\} ^{N-m} = exp[ - \beta \epsilon ] ^m##

Does this make sense?