Clausius summarized the thermodynamics laws 1st &2nd in the following sentences.
(a) The energy of the universe remains constant.
(b) The entropy of the universe tends towards a maximum.
In an isolated system, the entropy always increases and it is maximum at equilibrium state.
s isol = f(x)
where x is a parameter.
S isol = s max
at a point x = x eq
where X eq is the value of the parameter x at equilibrium state
So dS / dx = 0 at x = x eq represents e equilibrium state.
Thus dS = 0 at equilibrium state, it means at equilibrium state any conceivable change in entropy would be zero.