Author ORCID Identifier

https://orcid.org/0009-0005-3415-3042

Date of Award

Summer 8-31-2025

Document Type

Campus Access Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Physics, Applied

First Advisor

Jason R. Green

Abstract

Classical measurement is a process that we carry out on nature, where the outcome exists with a numerical value, and the process of the measurement is to determine it with the best uncertainty. The improvement in precision of estimating a parameter is directly related to the amount of information available about the parameter. Since the the lower bound in Cramér-Rao inequality is the method providing the optimal precision, higher information leads to an improved Cramér- Rao lower bound, and thus implies a more precise estimate of the parameter. Understanding sources of information is the key to improving the precision of classical measurements, especially for some deterministic dynamical systems that have a form of measurable uncertainty. In this dissertation, we introduce a Fisher information as a method to measure the amount of information which we can extract from a system, and determined by the local curvature and the phase speed at each point along the phase space trajectory. Once the general structure of classical trajectories is more fully understood, we establish a relationship between the rate of contraction for an ensemble of dissipative trajectories and the logarithmic derivative that evolves a classical density matrix in a dynamical system. We also show that not only quantum measurements are able to give more precise estimates than classical statistics, but classical mechanical measurements can also, in principle, give more precise estimates than purely statistical measurements. We derive a statistical-mechanical Fisher information that upper bounds the purely statistical Fisher information and leads to an optimal lower bound on the uncertainty of the state of classical dynamical systems. Then, we define ratios that measure the classical mechanical advantage in parameter estimation within classical systems enhancing classical precision, which involves improving the accuracy of measurements or estimations within the realm of classical physics.

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