Discrete fluctuations in memory erasure without energy cost

TL;DR

This paper investigates the discrete fluctuations in spin-based information erasure without energy cost, revealing exponential suppression of violations and a trade-off between fluctuation size and erasure cost.

Contribution

It introduces a detailed analysis of discrete fluctuations in VB erasure, deriving a Jarzynski-like equality and revealing the pronounced effects in highly polarized reservoirs.

Findings

Fluctuations below the VB bound are exponentially suppressed.

A Jarzynski-like equality for VB erasure is derived.

Discreteness of fluctuations is prominent in maximally polarized reservoirs.

Abstract

According to Landauer's principle, erasing one bit of information incurs a minimum energy cost. Recently, Vaccaro and Barnett (VB) explored information erasure within the context of generalized Gibbs ensembles and demonstrated that for energy-degenerate spin reservoirs, the cost of erasure can be solely in terms of a minimum amount of spin angular momentum and no energy. As opposed to the Landauer case, the cost of erasure in this case is associated with the discrete variable. Here we study the {\it discrete} fluctuations in this cost and the probability of violation of the VB bound. We also obtain a Jarzynski-like equality for the VB erasure protocol. We find that the fluctuations below the VB bound are exponentially suppressed at a far greater rate and more tightly than for an equivalent Jarzynski expression for VB erasure. We expose a trade-off between the size of the fluctuations and the cost of erasure. We find that the discrete nature of the fluctuations is pronounced in the regime where reservoir spins are maximally polarized. We also state the first laws of thermodynamics corresponding to the conservation of spin angular momentum for this particular erasure protocol. Our work will be important for novel heat engines based on information erasure schemes that do not incur an energy cost.