What characteristics define a chemical system in equilibrium?

Equality of forward and reverse rates.

For the reaction,

##A+BrarrC+D##;

there is a forward rate, ##K_f[A][B]##; and a reverse rate, ##K_r[C][D]##.

Equilibrium is defined the equality of forward and reverse rates.

i.e. ##K_f[A][B]####=####K_r[C][D]##

Or, ##K_f/K_r## ##=## ##([C][D])/([A][B])##

And ##K_f/K_r## ##=## ##K_(eq)##, ##"the equilibrium constant"##.