There is a known paradox in physics concerning time direction asymmetry.
Under microscopic laws of physics, i.e. particle physics, the laws that govern interactions between particles obey time symmetry. If you turn the time backward the particles will behave in exactly the same way. For example, an electron and anti-electron upon collision will annihilate each other and will create a photon. If however we turn axis of time backwards a photon will produce two particles that will fly away from each other. Both events, collision and birth of electron/anti-electron are observed in nature, in accelerometer experiments.
In macroscopic nature things are completely different. If you brake a glass, it will fly away into a myriad of pieces and that happens quite often, it just happened to me yesterday. However the reverse process of broken pieces assemble themselves into a whole glass have never been observed, at least so far.
Let's imagine the following mental experiment. What is particle physics is an approximation that explains particle interaction well enough. In that approximation a particle is an isolated atom that is independent on the rest of particles until interaction happens. In this picture the interaction is commutative:
a (x) b = b (x) a, where a and b are two states of the an atom before and after the interaction.
As a fact of the matter, we know that quantum field theory IS an approximation where some divergence in quantum electrodynamics. Integrals that describe particle interactions under higher number of corrections instead of converging to a more precise quantities, instead diverge into infinity.
If we get away from assumption of atom/particle independence and assume that particle state is always described by a matrix that describes both the particle and the world outside. The best example is quantum mechanics that describes a set of entangled states.
As we know matrix operations are in general not commutative:
A (x) B <> B (x) A
So the intuition of this concept is that time asymmetry is a direct consequence of particle state being matrix.