Physical Foundations of Landauer's Principle

We review the physical foundations of Landauer's Principle, which relates the loss of information from a computational process to an increase in thermodynamic entropy. Despite the long history of the Principle, its fundamental rationale and proper interpretation remain frequently misunderstood. Contrary to some misinterpretations of the Principle, the mere transfer of entropy between computational and non-computational subsystems can occur in a thermodynamically reversible way without increasing total entropy. However, Landauer's Principle is not about general entropy transfers; rather, it more specifically concerns the ejection of (all or part of) some correlated information from a controlled, digital form (e.g., a computed bit) to an uncontrolled, non-computational form, i.e., as part of a thermal environment. Any uncontrolled thermal system will, by definition, continually re-randomize the physical information in its thermal state, from our perspective as observers who cannot predict the exact dynamical evolution of the microstates of such environments. Thus, any correlations involving information that is ejected into and subsequently thermalized by the environment will be lost from our perspective, resulting directly in an irreversible increase in total entropy. Avoiding the ejection and thermalization of correlated computational information motivates the reversible computing paradigm, although the requirements for computations to be thermodynamically reversible are less restrictive than frequently described, particularly in the case of stochastic computational operations. There are interesting possibilities for the design of computational processes that utilize stochastic, many-to-one computational operations while nevertheless avoiding net entropy increase that remain to be fully explored.Comment: 42 pages, 15 figures, extended postprint of a paper published in the 10th Conf. on Reversible Computation (RC18), Leicester, UK, Sep. 201

Influence of Pr on the magnetic structure of Er

Time-of-flight neutron diffraction has been used to determine the temperature dependence of the magnetic structure of three binary hexagonal Er-Pr alloys, Er90Pr10, Er80Pr20, and Er60Pr40. In overall agreement with magneto-thermal measurements performed on these compounds, the addition of Pr initially increases the Curie temperature and decreases the Neel temperature, observed at 20 K and 86 K, respectively, for pure Er. The neutron diffraction data for Er90Pr10, however, also clearly show that a ferromagnetic phase, with moments parallel to the c-axis, coexists with modulated structure components, with increasing temperature up to 35 K, above which a pure sine modulated structure sets in up to the Neel temperature at approximately 65 K. A similar behavior is observed for Er80Pr20, where the sine modulated phase is observed to disappear at 48 K. In sharp contrast, only one magnetic phase, identified as ferromagnetic with moments parallel to the c-axis, is observed for Er60Pr40 from low temperatures up to the Curie point at 35 K. The propagation vectors of the sine modulated phases are found to be temperature dependent