We will show in this work that it is possible to perform a different treatment that
considers the internal energy as a functional of solely the density operator.
According to Ockham’s razor, this way of handling the first law is to be preferred to
the traditional one, since now one can dispense with, in order to describe the
thermodynamic work W, the two following theoretical assumptions (or needs) of the
traditional approach [3]: € explicit dependence of the Hamiltonian on some
‘‘external’’ parameters w, € recourse to the adiabatic theorem (AT) [3]. We can
summarize the AT contents as follows [3]: in the AT one regards the Hamiltonian as
depending on a parameter w that evolves in time from an initial value w1 to a final
value w2, during a time-interval t, in the fashion