  Simulations show Gly$_{15}$, a polypeptide lacking any side-chains, can
collapse in water. We assess the hydration thermodynamics in this collapse by
calculating the hydration free energy at each of the end points of the reaction
coordinate, here the end-to-end distance ($r$) in the chain. To examine the
role of the various conformations for a given $r$, we study the conditional
distribution, $P(R_g | r)$, of the radius of gyration for a given value of $r$.
$P(R_g|r)$ is found to vary more gently compared to the corresponding variation
in the excess hydration free energy. Using this insight within a multistate
generalization of the potential distribution theorem, we calculate a reasonable
upper bound for the hydration free energy of the peptide for a given $r$. On
this basis we find that peptide hydration greatly favors the expanded state of
the chain, despite primitive hydrophobic effects favoring chain collapse. The
net free energy of collapse is seen to be a delicate balance between opposing
intra-peptide and hydration effects, with intra-peptide contributions favoring
collapse by a small margin. The favorable intra-peptide interactions are
primarily electrostatic in origin, and found to arise primarily from
interaction between C=O dipoles, hydrogen bonding interaction between C=O and
N-H groups, and favorable interaction between N-H dipoles.
