On the adiabatic expansion of the visible space in a higher-dimensional Cosmology

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.