A similar question was asked here but mine is a bit different.
In thermodynamics, a mechanical equilibrium is defined as a uniform pressure (for a fluid).
In classical mechanics, equilibrium is defined by: sum of external forces equals to zero.
The link between the two is that no external forces work at an equilibrium. Why do we use pressure for the definition of thermodynamics, while it does not cover solid mechanics (because stress tensor is not a scalar tensor)? Would it be possible to give a global definition, compatible in both frameworks? I'm thinking of "an equilibrium is a state where all the macroscopic velocities are 0 with respect to an inertial frame". Unfortunately, this does not constitute a definition similar to common definitions of equilibrium in thermodynamics, which involve conjugate intensive and extensive quantities.