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 paper we focus on the antisymmetric contributions which describe isentropic oscillations with well-defined equations of motion. The formalism contains variables that are equivalent to momenta and coefficients that are analogous to inertial mass. We apply this formalism to simple problems with known answers such as an oscillating piston containing an ideal gas, and oscillations in an LC-circuit. 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.