| Summary: | Control of cooling and heating processes is essential in many industrial and biological processes. In fact, the time evolution of an observable quantity may differ according to the previous history of the system. For example, a system that is being subject to cooling and then, at a given time t _w for which the instantaneous temperature is $T({t}_{w})={T}_{\mathrm{st}}$ , is suddenly put in contact with a temperature source at T _st may continue cooling down temporarily or, on the contrary, undergo a temperature rebound. According to current knowledge, there can be only one ‘spurious’ and small peak/low. However, our results prove that, under certain conditions, more than one extremum may appear. Specifically, we have observed regions with two extrema and a critical point with three extrema. We have also detected cases where extraordinarily large extrema are observed, as large as the order of magnitude of the stationary value of the variable of interest. We show this by studying the thermal evolution of a low density set of macroscopic particles that do not preserve kinetic energy upon collision, i.e. a granular gas. We describe the mechanism that signals in this system the emergence of these complex and large memory effects, and explain why similar observations can be expected in a variety of systems.
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