# Cost of remembering a bit of information

## TL;DR

This paper presents a theoretical and experimental analysis of the energy required to preserve a single bit of information over time, highlighting the trade-offs imposed by quantum principles and refresh frequency.

## Contribution

It introduces a model and experiment to quantify the minimal energy for memory preservation, considering quantum limits and refresh strategies.

## Key findings

- Energy cost can be minimized with frequent refreshes
- Quantum uncertainty bounds memory lifetime
- Experimental validation of theoretical energy bounds

## Abstract

In 1961, Rolf Landauer pointed out that resetting a binary memory requires a minimum energy of $k_BT \ln(2)$. However, once written, any memory is doomed to loose its content if no action is taken. To avoid memory losses, a refresh procedure is periodically performed. In this paper we present a theoretical model and an experiment on a micro-electro-mechanical system to evaluate the minimum energy required to preserve one bit of information over time. Two main conclusions are drawn: i) in principle the energetic cost to preserve information for a fixed time duration with a given error probability can be arbitrarily reduced if the refresh procedure is performed often enough; ii) the Heisenberg uncertainty principle sets an upper bound on the memory lifetime.