Hamiltonian Memory: An Erasable Classical Bit

TL;DR

This paper demonstrates that a classical bit can be erased without thermodynamic cost by confining Hamiltonian dynamics to a single energy shell, challenging traditional views on the Landauer principle.

Contribution

It introduces a method to implement an erasable classical bit using Hamiltonian dynamics confined to a single energy shell, avoiding heat dissipation.

Findings

Erasable classical bits can be realized with Hamiltonian dynamics.

Probability concentration on a single energy shell enables thermodynamically free erasure.

Challenges the universality of the Landauer principle in specific Hamiltonian systems.

Abstract

Computations implemented on a physical system are fundamentally limited by the laws of physics. A prominent example for a physical law that bounds computations is the Landauer principle. According to this principle, erasing a bit of information requires a concentration of probability in phase space, which by Liouville's theorem is impossible in pure Hamiltonian dynamics. It therefore requires dissipative dynamics with heat dissipation of at least $k_BT\log 2$ per erasure of one bit. Using a concrete example, we show that when the dynamic is confined to a single energy shell it is possible to concentrate the probability on this shell using Hamiltonian dynamic, and therefore to implement an erasable bit with no thermodynamic cost.