arXiv subjects

Alexandra M. Jurgens

Publications and source records attributed to Alexandra M. Jurgens.

9 recordsLinked to original sources

arXiv2026

State Diagnostics of Complexity in Open Quantum Systems

We study the emergence of complexity in finite-size quantum systems as their dynamics transition from closed and coherent evolution to interacting and effectively open behavior. Using a state-based geometric framework, we represent mixed quantum states as probability measures on complex projective Hilbert space. This representation allows us to track how interactions reshape the underlying pure-state geometry. We introduce two complementary diagnostics: a distinguishability measure, based on the Wasserstein distance between probability-measure representations of mixed states, that quantifies sensitivity to initial states, and a state-space coverage index that measures long-time exploration of the subsystem state space. These diagnostics provide a geometric perspective on the emergence and evolution of quantum dynamical complexity. When applied to the quantum kicked top, both diagnostics generally increase with interaction strength. Their dependence on environment size is structured by parity symmetry, with integer-spin systems often exhibiting greater sensitivity and state-space coverage than half-integer-spin systems. These results highlight finite-size quantum effects and provide a geometric approach to quantifying dynamical complexity deep in the quantum regime

quant-ph↗

arXiv2024

Inferring Kernel $ε$-Machines: Discovering Structure in Complex Systems

Previously, we showed that computational mechanic's causal states -- predictively-equivalent trajectory classes for a stochastic dynamical system -- can be cast into a reproducing kernel Hilbert space. The result is a widely-applicable method that infers causal structure directly from very different kinds of observations and systems. Here, we expand this method to explicitly introduce the causal diffusion components it produces. These encode the kernel causal-state estimates as a set of coordinates in a reduced dimension space. We show how each component extracts predictive features from data and demonstrate their application on four examples: first, a simple pendulum -- an exactly solvable system; second, a molecular-dynamic trajectory of $n$-butane -- a high-dimensional system with a well-studied energy landscape; third, the monthly sunspot sequence -- the longest-running available time series of direct observations; and fourth, multi-year observations of an active crop field -- a set of heterogeneous observations of the same ecosystem taken for over a decade. In this way, we demonstrate that the empirical kernel causal-states algorithm robustly discovers predictive structures for systems with widely varying dimensionality and stochasticity.

cs.LG↗

arXiv2023

Whales in Space: Experiencing Aquatic Animals in Their Natural Place with the Hydroambiphone

Recording the undersea three-dimensional bioacoustic sound field in real-time promises major benefits to marine behavior studies. We describe a novel hydrophone array -- the hydroambiphone (HAP) -- that adapts ambisonic spatial-audio theory to sound propagation in ocean waters to realize many of these benefits through spatial localization and acoustic immersion. Deploying it to monitor the humpback whales (Megaptera novaeangliae) of southeast Alaska demonstrates that HAP recording provides a qualitatively-improved experience of their undersea behaviors; revealing, for example, new aspects of social coordination during bubble-net feeding. On the practical side, spatialized hydrophone recording greatly reduces post-field analytical and computational challenges -- such as the "cocktail party problem" of distinguishing single sources in a complicated and crowded auditory environment -- that are common to field recordings. On the scientific side, comparing the HAP's capabilities to single-hydrophone and nonspatialized recordings yields new insights into the spatial information that allows animals to thrive in complex acoustic environments. Spatialized bioacoustics markedly improves access to the humpbacks' undersea acoustic environment and expands our appreciation of their rich vocal lives.

q-bio.PE↗

arXiv2022

Whale Casting: Remote mobile streaming humpback whale vocalizations to the world

Over several days in early August 2021, while at sea in Chatham Strait, Southeast Alaska, aboard M/Y Blue Pearl, an online twitch.tv stream broadcast in real-time humpback whale vocalizations monitored via hydrophone. Dozens on mainland North American and around the planet listened in and chatted via the stream. The webcasts demonstrated a proof-of-concept: only relatively inexpensive commercial-off-the-shelf equipment is required for remote mobile streaming at sea. These notes document what was required and make recommendations for higher-quality and larger-scale deployments. One conclusion is that real-time, automated audio documenting whale acoustic behavior is readily accessible and, using the cloud, it can be directly integrated into behavioral databases -- information sources that now often focus exclusively on nonreal-time visual-sighting narrative reports and photography.

cs.HC↗

arXiv2021

Ambiguity Rate of Hidden Markov Processes

The $ε$-machine is a stochastic process' optimal model -- maximally predictive and minimal in size. It often happens that to optimally predict even simply-defined processes, probabilistic models -- including the $ε$-machine -- must employ an uncountably-infinite set of features. To constructively work with these infinite sets we map the $ε$-machine to a place-dependent iterated function system (IFS) -- a stochastic dynamical system. We then introduce the ambiguity rate that, in conjunction with a process' Shannon entropy rate, determines the rate at which this set of predictive features must grow to maintain maximal predictive power. We demonstrate, as an ancillary technical result which stands on its own, that the ambiguity rate is the (until now missing) correction to the Lyapunov dimension of an IFS's attractor. For a broad class of complex processes and for the first time, this then allows calculating their statistical complexity dimension -- the information dimension of the minimal set of predictive features.

cond-mat.stat-mech↗

arXiv2021

Divergent Predictive States: The Statistical Complexity Dimension of Stationary, Ergodic Hidden Markov Processes

Even simply-defined, finite-state generators produce stochastic processes that require tracking an uncountable infinity of probabilistic features for optimal prediction. For processes generated by hidden Markov chains the consequences are dramatic. Their predictive models are generically infinite-state. And, until recently, one could determine neither their intrinsic randomness nor structural complexity. The prequel, though, introduced methods to accurately calculate the Shannon entropy rate (randomness) and to constructively determine their minimal (though, infinite) set of predictive features. Leveraging this, we address the complementary challenge of determining how structured hidden Markov processes are by calculating their statistical complexity dimension -- the information dimension of the minimal set of predictive features. This tracks the divergence rate of the minimal memory resources required to optimally predict a broad class of truly complex processes.

cond-mat.stat-mech↗

arXiv2020

Shannon Entropy Rate of Hidden Markov Processes

Hidden Markov chains are widely applied statistical models of stochastic processes, from fundamental physics and chemistry to finance, health, and artificial intelligence. The hidden Markov processes they generate are notoriously complicated, however, even if the chain is finite state: no finite expression for their Shannon entropy rate exists, as the set of their predictive features is generically infinite. As such, to date one cannot make general statements about how random they are nor how structured. Here, we address the first part of this challenge by showing how to efficiently and accurately calculate their entropy rates. We also show how this method gives the minimal set of infinite predictive features. A sequel addresses the challenge's second part on structure.

nlin.CD↗

arXiv2020

Functional Thermodynamics of Maxwellian Ratchets: Constructing and Deconstructing Patterns, Randomizing and Derandomizing Behaviors

Maxwellian ratchets are autonomous, finite-state thermodynamic engines that implement input-output informational transformations. Previous studies of these "demons" focused on how they exploit environmental resources to generate work: They randomize ordered inputs, leveraging increased Shannon entropy to transfer energy from a thermal reservoir to a work reservoir while respecting both Liouvillian state-space dynamics and the Second Law. However, to date, correctly determining such functional thermodynamic operating regimes was restricted to a very few engines for which correlations among their information-bearing degrees of freedom could be calculated exactly and in closed form---a highly restricted set. Additionally, a key second dimension of ratchet behavior was largely ignored---ratchets do not merely change the randomness of environmental inputs, their operation constructs and deconstructs patterns. To address both dimensions, we adapt recent results from dynamical-systems and ergodic theories that efficiently and accurately calculate the entropy rates and the rate of statistical complexity divergence of general hidden Markov processes. In concert with the Information Processing Second Law, these methods accurately determine thermodynamic operating regimes for finite-state Maxwellian demons with arbitrary numbers of states and transitions. In addition, they facilitate analyzing structure versus randomness trade-offs that a given engine makes. The result is a greatly enhanced perspective on the information processing capabilities of information engines. As an application, we give a thorough-going analysis of the Mandal-Jarzynski ratchet, demonstrating that it has an uncountably-infinite effective state space.

cond-mat.stat-mech↗

arXiv2019

Measurement-Induced Randomness and Structure in Controlled Qubit Processes

When an experimentalist measures a time series of qubits, the outcomes generate a classical stochastic process. We show that measurement induces high complexity in these processes in two specific senses: they are inherently unpredictable (positive Shannon entropy rate) and they require an infinite number of features for optimal prediction (divergent statistical complexity). We identify nonunifilarity as the mechanism underlying the resulting complexities and examine the influence that measurement choice has on the randomness and structure of measured qubit processes. We introduce new quantitative measures of this complexity and provide efficient algorithms for their estimation.

quant-ph↗