Work as a memory record.

The possibility of a controlled manipulation with molecules at the nanoscale allows us to gain net work from thermal energy, although this seems to be in contradiction to the second law of thermodynamics. Any manipulation, however, causes some memory records somewhere in the system's surroundings. To complete the thermodynamic cycle, these records must be reset, which costs energy that cancels the previous gain. An important memory record may also be the final state of the work reservoir. This memory record is not reset. Nevertheless, it is rewritten and the associated memory erased whenever the state of the work reservoir is changed during the cycle repeating. The question is, what is the cost of this memory erasure. To answer it, we study a hypothetical cycle in which all memory records are reset except the state of the work reservoir alone, and the ensemble average of the work extracted from an equilibrium heat reservoir during this cycle, 〈W〉, is positive. It is shown that a strong information coupling of the system and the work reservoir then influences the system's dynamics so much that the cycle repeat may exhibit quite different behavior. Especially, it can run reversely and decrease energy in the work reservoir. It implies that even if the memory erasure is a natural part of the process, it costs energy in accord with information thermodynamics. At the nanoscale, this energy cost may manifest as a process obeying the fluctuation theorem.