In the elementary equations of the world, the arrow of time appears only where there is heat. The link between time and heat is... fundamental: every… - Carlo Rovelli

The thermal time hypothesis. In nature, there is no preferred physical time variable t. There are no equilibrium states ρ₀ preferred a priori. Rather, all variables are equivalent; we can find the system in an arbitrary state ρ; if the system is in a state ρ, then a preferred variable is singled out by the state of the system. This variable is what we call time.

But it isn’t absence that causes sorrow. It is affection and love. Without affection, without love, such absences would cause us no pain. For this reason, even the pain caused by absence is, in the end, something good and even beautiful, because it feeds on that which gives meaning to life.

The notion of time familiar to us may... be reconstructed in special physical situations, or within an approximation, as... the "surface of a liquid" disappears ...[at] the atomic level, or "temperature" ...makes sense only in certain physical situations and when there are enough degrees of freedom.