We're given a glass of water and addressed to put a few ink-drops in the glass. What is going to be the most general observations?
The question may appear tawdry. However, with little speculation one must come up with the following data.
'The ink slowly starts blending in the water without any eviction untill it thoroughly mixes'. This certainly is assertion. But the ink had an ordered state at the beginning when it was just put onto the water surface. And since any natural process always tends to move from a state of higher potential to that of a lower potential, the randomness of the ink must be stable that it being in a well defined arrangement!
We know that a natural process is irreversible. Heat flows from a hot body to a cold body, water falls naturally. These processes are not reversible in nature and do not turn around unless some external work is done. Perhaps this is the second law of thermodynamics. 'The change in entropy of an isolated system can never be negative'.
Our ink dot has already evolved by this time into greater randomness, perhaps so much of randomness that it is hard to spot it. But since it has moved naturally from an ordered state to a state of complete disorder, it must really admire disorder then, than order. Mayhap this is the direction of any natural process. Order → Disorder. And now it can be pointed out that our system, the glass and the ink-dot, had a more ordered state in the beginning than in the end. One might easily say that a state of order must exist before disorder, perhaps past and future. Thus randomness has now become a way to distinguish the past and the future!
According to the Big Bang theory, the Universe was initially very hot with energy distributed uniformly. For a system in which gravity is important, such as the universe, this is a low-entropy state. As the Universe grows, its temperature drops, which leaves less energy available to perform work in the future than was available in the past. Additionally perturbations in the energy density grow eventually forming galaxies and stars. Thus the Universe itself has a well-defined thermodynamic arrow of time.
We're all moving from state of order to complete disorder and randomness. And perhaps this is the way of nature, this is the arrow, the direction of time.