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I am struggling in deriving the WHAM equations. Among others, I follow this paper by Kumar et al. In the appendix, in eq. 24 they write the density of states as a weighted sum over the "measured" density of states of different simulations. The weights are $\omega_j(\{V\})$. My question is, why are the weights $V$-dependent? The same question arises when looking at the Ferrenberg and Swendsen paper (unfortunately not publicly available), in eq. (1). Here they write the weights as $p_n(S)$, but again, they are $S$-dependent. Why aren't these weights just constant?

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