Equation for the Arrow of Time

Entropy, as defined by Rudolph Clausius and expounded upon by Ludwig Boltzmann, whose grandfather was a watchmaker, is sometimes referred to by physicists as "time's arrow" or the "arrow of time".

The equation is a distillation of the second law of thermodynamics. Delta S is always greater than or equal to zero (ΔS ≥ 0). The state variable, S, being a measurable and calculable quantity in an isolated process that increases or remains the same but never decreases.

The second law asserts that thermodynamic processes occur in a specific direction. Heat energy passes from hot bodies to cold bodies, not the other way around.

As Carlo Rovelli phrased it in The Order of Time:

It is the only equation of fundamental physics that knows any difference between past and future. The only one that speaks of the flowing of time.

Time passes in the same direction that entropy increases.