Rephrasing the Second law of thermodynamics as a maximizing principle According to the second of thermodynamics
$$dS\geq 0\ \ \ \ \text{Isolated Process}$$
Is it write to say,

If the given system $S$ goes from state $A$ to state $B$, then the path taken by the system is the one in which entropy is maximized.

To me, it's No, Since the law says that entropy can't decrease but it doesn't say that it has to change by maximum.
 A: According to the usual thermodynamics, the cited sentence, without further qualifications, is meaningless.
Entropy is a function of the state. It is meaningful to speak about the initial and final entropy for any transformation starting and ending in equilibrium states. There is no reason to believe, in general, that during the transformation, the system is continuously close to equilibrium states. Therefore, there is no control over the path. Even worse, in a non-equilibrium transformation, there is no path at all in the space of thermodynamic variables.
A: A statement such as "If the given system S goes from state A to state B, then the path taken by the system is the one in which entropy is maximized," cannot be true in general without specifying that in a sufficiently small neighborhood of the path taken there is only one stable equilibrium point. In that case the statement of maximum is really just that the entropy as function of the state variables is a convex one, that is its second derivative matrix $\frac{\partial ^2 S}{\partial x_k \partial x_m}$is negative definite where $x_k$ are the extensive parameters of the system.
On the contrary, if there are multiple locally stable equilibrium points accessible then there is no guarantee that the natural path compatible with the constraints will seek out the one with the largest entropy. One can say only then that the entropy is maximized within a sufficiently small neighborhood of the equilibrium point.
A: If a given closed system goes from equilibrium state  to equilibrium state , then the change in entropy between these states is the maximum of the integral of $dq/T_{boundary}$ over all the possible paths taken by the system between these two end states.  Here, $T_{boundary}$ is the temperature at the boundary of the system (with its surroundings) through which the heat dq flows.
