Shake a thin layer of grains and let it reach a steady temperature. Now change the shaking intensity — reduce the amplitude — and watch. The granular temperature drops, but not monotonically. There is a bump: the system briefly heats up before cooling to its new steady state. The system remembers its previous conditions, and the memory manifests as a temporary deviation from the expected relaxation path.
Vega Reyes et al. (arXiv:2602.20716) demonstrate this Kovacs memory effect experimentally in vibrated granular matter and trace its physical origin. The memory lives in the coupling between horizontal and vertical temperature components. When the shaking changes, the two components relax at different rates. The fast relaxation (vertical, directly driven) and the slow relaxation (horizontal, coupled indirectly) fall out of synchronization. The temporary desynchronization produces the bump — the system's “memory” of where it was.
Then the memory disappears. Once the fast and slow components re-synchronize — when the system enters the hydrodynamic regime where only the total temperature matters — the relaxation becomes memoryless. The future depends only on the current state, not the history. The Kovacs effect is confined to the initial fast relaxation stage. It is a transient phenomenon, not a persistent one.
The mechanism reveals something general about memory in physical systems. Memory exists in the coupling between degrees of freedom that relax at different rates. When those degrees of freedom are out of equilibrium with each other, the system carries information about its past in their relative values. When they equilibrate, the information is erased. Memory is a property of non-equilibrium — of unfinished relaxation between internal components.
This defines two temporal regimes: a kinetic regime where the system has memory (internal degrees of freedom are still coupled and desynchronized) and a hydrodynamic regime where it does not (they have equilibrated and only aggregate quantities matter). The transition between them is the expiration of memory. Not gradual fading but a regime change.