Is it impossible to design an importer protein that can selectively import certain molecules without using energy? If not, why?

Ans.:
Cell has high concentration of different substances, it requires energy (we have to do it forcibly, and will not occur spontaneously by itself) so it has some energy stored in this way.
One of the fundamental principles of physics is that entropy of the universe never decreases. To continue living, cell has to concentrate some definite substances inside the cell; this process leads to a decrease in entropy. So according to aforesaid principle, entropy must increase in some other processes. Entropy can increase by simultaneous diffusion of some other substances or simply by dissipation of energy- namely heat. So in principle, it is impossible to design an importer protein that can selectively import certain molecules without using energy of any form (energy can be stored in concentration gradient which can also be harnessed in active transport process).