Absolute entropy of a system is calculated either by integrating heat capacity/temp at constant pressure from 0kelvin to the measured temperature, or by calculating via Shannon's method using average amount of information in a discrete random variable.
There is no time factor in any absolute entropy equation.
Empirically, if you measure the entropy of a closed system at a given time, and you measure the entropy of that same closed system at a different time, then calculate the deltas of each, their signs match so long as the time delta is finite and the system isn't empty. So stated plainly, as time increases, so does entropy.
By combining these first principle formulae with the empirical results on entropy, you arrive at the second law of thermodynamics. However, like I said before, we're not really sure why the signs match and it's considered to be an unsolved problem in physics.
