  One problem in the application of the Skyrme model to nuclear physics is that
it predicts too large a value for the compression modulus of nuclear matter.
Here we investigate the thermodynamics of the BPS Skyrme model at zero
temperature and calculate its equation of state. Among other results, we find
that classically (i.e. without taking into account quantum corrections) the
compressibility of BPS skyrmions is, in fact, infinite, corresponding to a zero
compression modulus. This suggests that the inclusion of the BPS submodel into
the Skyrme model lagrangian may significantly reduce this too large value,
providing further evidence for the claim that the BPS Skyrme model may play an
important role in the description of nuclei and nuclear matter.
