  In the context of higher-dimensional cosmologies with isotropic visible and
internal space and multi-perfect fluid matter, we study the conditions under
which adiabatic expansion of the visoble external space is possible, when a
time-dependent internal space is present. The analysis is based on a
reinterpretation of the four-dimensional stress-energy tensor in the presence
of the extra dimensions. This modifies the usual adiabatic energy conservation
laws for the visible Universe, leading to a new type of cosmological evolution
which includes large-scale entropy production in four dimensions.
