  Eliashberg theory is used to investigate the range of thermodynamic
properties possible within a two-band model for s-wave superconductivity and to
identify signatures of its two-band nature. We emphasize dimensionless BCS
ratios (those for the energy gaps, the specific heat jump and the negative of
its slope near Tc, the thermodynamic critical field Hc(0), and the normalized
slopes of the critical field and the penetration depth near Tc), which are no
longer universal even in weak coupling. We also give results for
temperature-dependent quantities, such as the penetration depth and the energy
gap. Results are presented both for microscopic parameters appropriate to MgB2
and for variations away from these. Strong coupling corrections are identified
and found to be significant. Analytic formulas are provided which show the role
played by the anisotropy in coupling in some special limits. Particular
emphasis is placed on small interband coupling and on the opposite limit of no
diagonal coupling. The effect of impurity scattering is considered,
particularly for the interband case.
