  Second law of thermodynamics imposes that in any thermodynamic process the
entropy production must be nonnegative. In continuum physics such a requirement
is fulfilled by postulating the constitutive equations which represent the
material properties of the bodies in such a way that second law of
thermodynamics is satisfied in arbitrary processes. Such an approach, first
assumed in some pioneering papers by Coleman and Noll \cite{ColNol} and Coleman
and Mizel \cite{ColMiz}, in practice regards second law of thermodynamics as a
restriction on the constitutive equations, which must guarantee that any
solution of the balance laws satisfies also the entropy inequality. As observed
by Muschik and Ehrentraut \cite{MusEhr}, this is a useful operative assumption,
but not a consequence of general physical laws. Indeed, a different point of
view, which regards second law of thermodynamics as a restriction on the
thermodynamic processes, i.e., on the solutions of the system of balance laws,
is possible. This is tantamount to assume that there are solutions of the
balance laws which satisfy the entropy inequality, and solutions which do not
satisfy it. In order to decide what is the correct approach, Muschik and
Erhentraut postulated an amendment to the second law, which makes explicit the
evident but rather hidden assumption that in any point of the body the entropy
production is zero if, and only if, this point is thermodynamic equilibrium.
Then they proved that, given the amendment, second law of thermodynamics is
necessarily a restriction on the constitutive equations and not on the
thermodynamic processes. In the present paper we revisit their proof, lighting
up some geometric aspects which were hidden in Ref. \cite{MusEhr}. Moreover, we
propose an alternative formulation of second law of thermodynamics which
incorporates the amendment.
