Arrow of Time

Arrow of Time:
Why do we perceive time as always moving forward? Why are our
memories always of the past and never of the future? All the
fundamental Newtonian laws are time reversible. Collisions look the
same forwards or backwards. A box of gas molecules obeying Newton's
laws perfectly does not have an inbuilt arrow of time. However, it is
possible to show that the continual random molecular motions will
cause the entire ensemble to visit and revisit every possible state of the
box, much like the continual shuffling of a deck of cards will eventually
reproduce any sequence.

This ability of Nature to be divided into a multitude of states makes it
easier to understand why thermodynamical systems move toward
equilibrium, known as Poincare's theorem. If a box of gas is in a low
entropy state at one moment, it will very probably soon be in a less
ordered state since given the large number of states for it to evolve to,
most of those states are of higher entropy. So just by the laws of chance,
the box has a higher probability of becoming a higher entropy state
rather than a lower one since there are so many more possible high
entropy states.
Poincare's theorem claims that if every individual state has the same
chance of being visited, then obviously mixed-up states are going to
turn up much more often than the less mixed-up or perfectly ordered
states, simply because there are many more of them.

Thermodynamical events, such as a growing tree, are not reversible.
Cracked eggs do not repair themselves. Defined by these events, time
has an arrow, a preferred direction.
Entropy and the arrow of time are strongly linked. Increasing entropy is
in the direction of positive time. However, a study of the components to
systems shows that the parts are describable in terms of time-symmetric
laws. In other words, the microscopic world is ruled by time-symmetric
laws, but the macroscopic world has a particular direction.