Giuseppe D'Adamo, Andrea Pelissetto, Carlo Pierleoni
We reconsider the structure-based route to coarse graining in statistical mechanics and elucidate the failure of state-dependent potentials to reproduce the correct thermodynamics of the underlying original system. Requiring only that the interactions in the original model be state independent, we prove that any coarse-graining procedure producing state-dependent pair interactions is unable to provide the correct thermodynamics of the original system. Moreover, we show that the state- dependent potentials depend on the ensemble in which they have been derived. Therefore, care must be used in applying canonical state-dependent potentials to predict phase lines, which is typically performed in other ensembles.
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http://arxiv.org/abs/1211.2694
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