  We present a maximum entropy approach to analyze the internal dynamics of a
small system in contact with a large bath e.g. a solute-solvent system. For the
small solute, the fluctuations around the mean values of observables are not
negligible and the probability distribution P(r) of the state space depends on
the intricate details of the interaction of the solute with the solvent. Here,
we employ a superstatistical approach: P(r) is expressed as a marginal
distribution summed over the variation in {\beta}, the inverse temperature of
the solute. The joint distribution P({\beta},r) is estimated by maximizing its
entropy. We also calculate the first order system-size corrections to the
canonical ensemble description of the state space. We test the development on a
simple harmonic oscillator interacting with two baths with very different
chemical identities viz. a) Lennard-Jones particles and b) water molecules. In
both cases, our method captures the state space of the oscillator sufficiently
well. Future directions and connections with traditional statistical mechanics
are discussed.
