  In this work we study in a formal way the density dependent hadron field
theory at finite temperature for nuclear matter. The thermodynamical potential
and related quantities, as energy density and pressure are derived in two
different ways. We first obtain the thermodynamical potential from the grand
partition function, where the Hamiltonian depends on the density operator and
is truncated at first order. We then reobtain the thermodynamical potential by
calculating explicitly the energy density in a Thomas-Fermi approximation and
considering the entropy of a fermi gas. The distribution functions for
particles and antiparticles are the output of the minimization of the
thermodynamical potential. It is shown that in the mean field theory the
thermodynamical consistency is achieved. The connection with effective chiral
lagrangians with Brown-Rho scaling is discussed.
