The laws of nature, except the second law of thermodynamics, are symmetric in time. Reversing the time in the dynamical equations of motion simply describes everything going backwards. The second law is different. Entropy must never decrease in time, except statistically and briefly.

Many natural processes are apparently irreversible. Irreversibility is intimately connected to the direction of time. Identifying the physical reasons for the observed irreversibility, the origin of irreversibility, would contribute greatly to understanding the apparent asymmetry of nature in time, despite nature’s apparently perfect symmetry in space.

In 1927, Arthur Stanley Eddington coined the term “Arrow of Time” in his book The Nature of the Physical World. He connected “Time’s Arrow” to the one-way direction of increasing entropy required by the second law of thermodynamics. This is now known as the “thermodynamic arrow.”
(Nature of the Physical World, 1927, p.328-9)

In his later work, Eddington identified a “cosmological arrow,” the direction in which the universe is expanding, as shown by Edwin Hubble about the time Eddington first defined the thermodynamic arrow. New Pathways in Science, 1937, p.328-9)

There are now at least five other proposed arrows of time (discussed below). We can ask whether one arrow is a “master arrow” that all the others are following, or perhaps time itself is just a given property of nature that is otherwise irreducible to something more basic, as is space.

Given the four-dimensional space-time picture of special relativity, and given that the laws of nature are symmetric in space, we may expect the laws to be invariant under a change in time direction. The laws do not depend on position in space or direction, they are invariant under translations and rotations, space is assumed uniform and isotropic. But time is not just another spatial dimension. It enters into calculations of event separations as an imaginary term (multiplied by the square root of minus 1). Nevertheless, all the dynamical laws of motion are symmetric under time reversal.

So the basic problem is – how can macroscopic irreversibility result from microscopic processes that are fundamentally reversible?