Our paper discussed in the previous blog post might prompt this question: Is there still a way to use Landauer’s principle to convert the free energy of a system to its bit erasure capacity? The answer is “yes”, which we can demonstrate with a simple argument.

**Summary**: The correct measure of bit-erasure capacity *N* for an isolated system is the negentropy, the difference between the system’s current entropy and the entropy it would have if allowed to thermalize with its current internal energy. The correct measure of erasure capacity for a constant-volume system with free access to a bath at constant temperature is the Helmholtz free energy (divided by , per Landauer’s principle), provided that the additive constant of the free energy is set such that the free energy vanishes when the system thermalizes to temperature . That is,

where and are the internal energy and entropy of the system if it were at temperature . The system’s negentropy lower bounds this capacity, and this bound is saturated when .

Traditionally, the Helmholtz free energy of a system is defined as , where and are the internal energy and entropy of the system and is the constant temperature of an external infinite bath with which the system can exchange energy.^{a } (I will suppress the “Helmholtz” modifier henceforth; when the system’s pressure rather than volume is constant, my conclusion below holds for the Gibbs free energy if the obvious modifications are made.)

However, even in the case of fixed bath temperature, we cannot naively use Landauer’s principle to divide the free energy by to get the erasure capacity.… [continue reading]