Given condition

The resultant external force on the system is zero: $\sum \vec F_{\text{ext}} = 0$

For a system of particles, the rate of change of total linear momentum is $\frac{d\vec P}{dt} = \sum \vec F_{\text{ext}}$

Therefore, $\frac{d\vec P}{dt} = 0 \implies \vec P = \text{constant}$

So the linear momentum of the system does not change with time.

Check option A

Option A states: Linear momentum of the system does not change in time.

This follows directly from $\frac{d\vec P}{dt} = 0$

Hence, A is correct.

Check option B

Option B states: Kinetic energy of the system does not change in time.

This is not necessarily true. Even if net external force is zero, internal forces may do work and redistribute energy within the system.

Example: an explosion of a body initially at rest. The net external force is zero, but kinetic energy increases due to internal energy conversion.

Hence, B is incorrect.

Check option C

Option C states: Angular momentum of the system does not change in time.

For angular momentum, $\frac{d\vec L}{dt} = \vec \tau_{\text{ext}}$

Zero net external force does not imply zero external torque.

Example: two equal and opposite external forces form a couple. Then net force is zero, but torque is nonzero, so angular momentum changes.

Hence, C is incorrect.

Check option D

Option D states: Potential energy of the system does not change in time.

This is also not necessarily true. Internal configuration may change, causing potential energy to change, even when net external force is zero.

Example: two particles interacting via a spring can move relative to each other; spring potential energy changes while net external force on the system remains zero.

Hence, D is incorrect.

Final conclusion

The only statement that can surely be said is: $\boxed{A}$