  The field-dependent equilibrium thermodynamics is derived with two methods:
either by using the potential formalism either by the statistical method.
Therefore, Pontrjagin's extremum principle of control theory is applied to an
extended ensemble average. This approach allows to derive the grand partition
function of thermodynamics as a result of a control problem with the Hamilton
energy. Furthermore, the maximum entropy principle follows and the second law
in a modified form. The derivation can predict second law violations if cycles
with irreversibilities in varying potential fields are included into
consideration. This conclusion is supported indirectly by experimental data
from literature. The upper maximum gain efficiency of a cycle with a known
polymer solution as dielectrics was estimated to less than 1 promille per
cycle. Note added in proof 28th October 2003: Comparing this preprint work with
an analogous ferrofluidic system discrepancies are is found which show that the
concrete model proposed here in section 4 is insufficient to settle the
question. A way to solve the problem is proposed.
