  The amoeba of a complex hypersurface is its image under a logarithmic
projection. A number of properties of algebraic hypersurface amoebas are
carried over to the case of transcendental hypersurfaces. We demonstrate the
potential that amoebas can bring into statistical physics by considering the
problem of energy distribution in a quantum thermodynamic ensemble. The
spectrum ${\epsilon_k}\subset \mathbb{Z}^n$ of the ensemble is assumed to be
multidimensional; this leads us to the notions of a multidimensional
temperature and a vector of differential thermodynamic forms. Strictly
speaking, in the paper we develop the multidimensional Darwin and Fowler method
and give the description of the domain of admissible average values of energy
for which the thermodynamic limit exists.
