Thermodynamics is a macroscopic theory.
But any macroscopic level is a consequence of the microscopic
description of an extensive (macroscopic) system. Hence, if we
choose such a microscopic description
that the Entropy begins to decrease, we will violate
Thermodynamics Second Law. We cannot do it
because this Second Law is mathematically proven.
Otherwise, the Thermodynamics Second Law “Entropy Grows”
must be accompanied with
this text "the law holds absolutely for all initial states (such
states are microscopic descriptions of a large system), except just
one or two." But this is absurd. It would not be a reliable law.
Hence T-symmetry is violated on microscopic description
of an extensive system.
Another idea is this: the arrow of time
is the increase of information in an observer's brain.
Time is directed in the direction where data in
the brain is growing. That is why they say that old enough
humans fall back into childhood.
Then the reverse of time's arrow
means that the information in the brain becomes vanishing.
But that violates the definition of the time's arrow.
Hence, we cannot reverse time. So, there must be
T-asymmetry on every level of nature.
Nobody knows how our Universe came to be
because the antimatter is missing.
In the Big Bang, an equal amount of matter and antimatter
should have been, unless there is a CP symmetry violation.
But because the CPT-symmetry cannot be violated,
the violation of CP means the violation of the time-reverse
Thermodynamics says that Entropy must grow
(or stay the same). This conclusion does not depend
on the initial condition of a system. Hence, we cannot fine-tune
velocities and positions of the particles in the system to decrease
Entropy. For example, we cannot achieve such a situation
when if you eat food, the food comes out of your mouth.
And when you drink water from a glass the water comes into the glass.
Therefore, even if we can reverse a
movie on the VCR recorder, we cannot reverse the progress of
the real world.
Therefore, there is time Asymmetry, the T-symmetry violation.
Such T-violation means that Hawking's Information Loss
Paradox at Black Holes is not a paradox but a law of Nature.
If we lose information, we cannot reverse the time.
But we cannot reverse time. Hence, we lose information.
Let us suppose that John lands on a distant planet, where time runs backward.
Then he meets Bob on this planet. Bob's home is this alien planet.
But because time runs backward, the data inside Bob's brain constantly vanishes.
But this is impossible. Hence, there is no place where time runs backward.
Yes, the locally measured Entropy can decrease, but the arrow of time cannot
revert its direction.