Landauer’s Principle and Divergenceless Dynamical Systems

Abstract

Landauer's principle is one of the pillars of the physics of information. It constitutes one of the foundations behind the idea that "information is physical". Landauer's principle establishes the smallest amount of energy that has to be dissipated when one bit of information is erased from a computing device. Here we explore an extended Landauerlike principle valid for general dynamical systems (not necessarily Hamiltonian) governed by divergenceless phase space flows.

Classical analogue of the statistical operator

“…We are specially interested in dynamical systems with divergenceless phase-space flows, which encompass Hamiltonian systems amongst their members and are characterized by the fact that their dynamics is informationconserving [25]. Indeed, divergenceless dynamical systems constitute the classical version of dynamical systems where information is preserved during the time evolution of the system.…”

Introductory Chapter: Physics of Information and Quantum Mechanics - Some Remarks from a Historical Perspective

“…This is nicely summarized in Landauer's famous motto "information is physical" [18]. Landauer principle has been the focus of intense research activity, and has been extended and generalized in diverse directions (see, for instance, [19] and references therein). Interest in the connections between physics and information increased substantially with the discovery that quantum mechanics allows for novel and highly counter-intuitive ways of transmitting and processing information.…”