Mechanics of memory of an information engine

Single particle heat engines are the essential building blocks to understand the information processing in biological systems. As a biological process typically involves transition among multiple states spanning over widely different timescales, the cumulative outcome is naturally expected to depend crucially on the memory of the dominant previous states. We attempt to model such intrinsic memory by introducing a two-step fast transition where the two steps are separated by a waiting time. The system then slowly relaxes to its final state. A complementary reverse protocol is considered to ensure the return of the system to its initial state. Note that such a cycle is fundamentally different from those performing under the feedback due to delayed measurements. Contrary to the latter case, the case of intrinsic memory has got very little attention so far. Primary focus of this study is to elucidate the mechanical aspects of the intrinsic memory processes in terms of the space-time correlation functions. The operational space and states of such an information engine is also explored as a function of the waiting time for the memory formation.