I am a bit confused with the description of the thermodynamic equilibrium from my course. By definition the system is in equilibrium if all state parameters are constant in time and there are no flows in the system (otherwise it will be a stationary process). But I cannot understand why thermodynamic equilibrium of a system is equivalent to existence of an equation $F(a_1,a_2,...,a_p)=0$, where $a_1,a_2,...,a_p$ are state parameters.
This was used to formulate the 0th law of thermodynamic, that if for systems A, B, C pair of them (A,B) is in equilibrium and (B,C) as well, so one can write
there exists function $F_3$ such that $F_3(a_1,a_2,...,a_p;c_1,c_2,...,c_r)=0$, what means that the pair of systems (A,C) is in equilibrium.
My thinking is that one can rather easily find such functions, for example, $a_1(t)$ and $a_2(t)$ that $F(a_1(t),a_2(t),...,a_p)=0$ however the system will not be in equilibrium.