Information Devices Based on Quantized Liénard-Hermite Oscillators

Abstract

Information has both theoretical and natural importance. At it’s roots from both a theoretical and quantum mechanical perspective, information is a dynamical process that is governed by a coupled relationship between energy and entropy. This research will investigate means for synthesizing information that is consistent with both quantum mechanical and dynamical processes. Such an approach is expected to be more consistent with naturally occurring systems, such as chemical and biological ones. The precise relationship between multiple stable equilibriums, energy quanitzation and stable information bearing patterns in the phase plane are examined. Relationships to information theory are a logical application of these results. The theorem provided allows for physical realizations of actual continuous-time quantized computational devices that are consistent with atomic and molecular dynamical processes. This pursuit can be thought of as the development of an electronic device that behaves according to quantum dynamical behaviors similar to molecular orbit phenomenology. The motivation for such devices is derived from an interest in developing a dynamical process that adheres to what will be described as physical means for representing the dynamical process of information. Results from actually synthesized physical devices are also provided. Collectively, these results represent the first known characterization and synthesis of a quantum mechanical facsimile for a naturally occurring information bearing dynamical system.