Thermodynamics of memory erasure via a spin reservoir

TL;DR

This paper explores the thermodynamics of information erasure using a spin reservoir, introducing the concepts of spinlabor and spintherm, and deriving bounds and fluctuation theorems for these quantities.

Contribution

It clarifies the costs of spin-based erasure, derives bounds for spinlabor, and generalizes fluctuation theorems in the context of spin reservoirs.

Findings

The bound on erasure cost can be violated by spinlabor, but not by spintherm.

Three bounds for spinlabor are derived, with the tightest identified.

A generalized Jarzynski equality and violation probability are established.

Abstract

Thermodynamics with multiple-conserved quantities offers a promising direction for designing novel devices. For example, Vaccaro and Barnett's [J. A. Vaccaro and S. M. Barnett, Proc. R. Soc. A 467, 1770 (2011); S. M. Barnett and J. A. Vaccaro, Entropy 15, 4956 (2013)] proposed information erasure scheme, where the cost of erasure is solely in terms of a conserved quantity other than energy, allows for new kinds of heat engines. In recent work, we studied the discrete fluctuations and average bounds of the erasure cost in spin angular momentum. Here we clarify the costs in terms of the spin equivalent of work, called spinlabor, and the spin equivalent of heat, called spintherm. We show that the previously-found bound on the erasure cost of $\gamma^{-1}\ln{2}$ can be violated by the spinlabor cost, and only applies to the spintherm cost. We obtain three bounds for spinlabor for different erasure protocols and determine the one that provides the tightest bound. For completeness, we derive a generalized Jarzynski equality and probability of violation which shows that for particular protocols the probability of violation can be surprisingly large. We also derive an integral fluctuation theorem and use it to analyze the cost of information erasure using a spin reservoir.