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.