  We generalize the method introduced in J. Phys. A: Math. Gen. 35, 7255 (2002)
based on the concept of thermodynamic equivalence and we transform a Fermi
system of general density of states into a thermodynamically equivalent Bose
system. This consists of mapping configurations of fermions from the original
system onto configurations of bosons, the initial and final configurations
having the same energy above the many-body ground state energy. In this way we
obtain two systems of particles of different exclusion statistics, but which
have the same entropies--and therefore identical canonical thermodynamic
properties. This method enables one in general to calculate the system
properties in either of the bosonic and fermionic representations.
  We check the method here in microscopic detail by calculating the equilibrium
particle distributions in the two representations using the entropy
maximization at fixed particle number and fixed ``fermionic'' and ``bosonic''
energies, respectively. Analytical calculations seem difficult to do, but we
check the results numerically and we find them equal within the numerical
accuracy.
