Why does isentropic correspond to adiabatic?

Think about adding heat as adding kinetic energy, that mixes it up like stirring a soup. If you stir the soup with some kinetic energy, entropy increases. If you add no kinetic energy, then it won't be stirred and entropy will stay the same. Hence the formula from Breno (well someone else originally but you get the idea). The basic idea of the 2nd law of thermodynamics is that energy (heat) is always flowing through the universe, mixing things up. So yes with time everything increases in entropy, assuming energy is flowing through it as it always is in our universe, but its not a constant increase in entropy and can at times be 0 in a perfectly insulated system (should we able to create such a system)