Response to "Comment on 'Zero and negative energy dissipation at information-theoretic erasure'"

TL;DR

This paper clarifies that information entropy and thermodynamic entropy are distinct, showing that energy dissipation during erasure does not directly relate to information entropy changes, especially in deterministic systems.

Contribution

It proves that information entropy cannot generally be linked to energy dissipation limits and clarifies the difference between information and thermodynamic entropy during erasure.

Findings

Information entropy remains zero in deterministic, error-free erasure.

During thermalization, entropy increases to one bit, but energy dissipation remains positive.

Information entropy and thermodynamic entropy are fundamentally different quantities.

Abstract

We prove that statistical information theoretic quantities, such as information entropy, cannot generally be interrelated with the lower limit of energy dissipation during information erasure. We also point out that, in deterministic and error-free computers, the information entropy of memories does not change during erasure because its value is always zero. On the other hand, for information-theoretic erasure - i.e., "thermalization" / randomization of the memory - the originally zero information entropy (with deterministic data in the memory) changes after erasure to its maximum value, 1 bit / memory bit, while the energy dissipation is still positive, even at parameters for which the thermodynamic entropy within the memory cell does not change. Information entropy does not convert to thermodynamic entropy and to the related energy dissipation; they are quantities of different physical nature. Possible specific observations (if any) indicating convertibility are at most fortuitous and due to the disregard of additional processes that are present.