Irreversibility as a Law of Nature

The fundamental laws of physics are time-reversal invariant. The arrow of time and the definiteness of measurement outcomes are therefore usually attributed to assumptions outside the dynamics: coarse-graining with a low-entropy initial state, and a collapse postulate or an observer. We propose instead that irreversibility is itself a law of nature. Time evolution is a semigroup. An entry, once made, cannot be undone, and an earlier state can recur only through a new forward process, suppressed by $e^{-\Delta S/k_B}$. The entropy entered in the causal past forms a scalar memory field, which defines the direction of time at every event. We state the dynamical law without new dimensional constants. Entries occur where energy enters a quantum-chaotic subsystem and produces entropy. Their rate is bounded by the Thouless time. Free fields, integrable systems and matter in equilibrium are left unchanged. An entry selects an energy window with the Born weight and makes the time average within it final. The resulting dynamics is linear and completely positive on the joint space of state and record. It gives definite outcomes for measurements that transfer energy, without an observer. The theory predicts that, after an entry, even a perfect time reversal recovers the initial state only with a probability of order $e^{-\Delta S/k_B}$, whereas standard quantum mechanics predicts complete recovery. A model calculation confirms this as a proof of concept. If gravity is sourced by what has been entered, it neither entangles nor decoheres cold, freely falling masses. Elements still set by hand, and the open problems of the gravitational part, are stated explicitly.