  Onsager's phenomenological equations successfully describe irreversible
thermodynamic processes. They assume a symmetric coupling matrix between
thermodynamic fluxes and forces. It is easily shown that the antisymmetric part
of a coupling matrix does not contribute to dissipation. Therefore, entropy
production is exclusively governed by the symmetric matrix even in the presence
of antisymmetric terms. In this work we focus on the antisymmetric
contributions which describe isentropic oscillations and well-defined equations
of motion. The formalism contains variables that are equivalent to momenta, and
coefficients that are analogous to an inertial mass. We apply this formalism to
simple problems such as an oscillating piston and the oscillation in an
electrical LC-circuit. We show that isentropic oscillations are possible even
close to equilibrium in the linear limit and one does not require far-from
equilibrium situations. One can extend this formalism to other pairs of
variables, including chemical systems with oscillations. In isentropic
thermodynamic systems all extensive and intensive variables including
temperature can display oscillations reminiscent of adiabatic waves.
