On the Gravitational Hysteresis in the Kinetic Theory

General theory of relativity is non–linear in nature and therefore can result in hysteresis-like effects and cause systems to remember the footprint of the gravitational field. Here we have investigated this effect using the Kinetic theory in curved spacetime. It is shown that the entropy rate experiences this hysteresis behavior. The effect is then considered for some special spacetimes, including Schwarzschild black hole, Friedmann–Lemaître–Robertson–Walker cosmological solution, and the flat Minkowski spacetime perturbed by a gravitational wave pulse. It is shown that there is some hysteresis effect for the entropy rate.