京都大学 / 新制・課程博士 / 博士(理学) / 甲第24400号 / 理博第4899号 / 新制||理||1700(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 佐々 真一, 教授 早川 尚男, 准教授 藤 定義 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

The project concerns the study of the interplay among quantum mechanics, statistical mechanics and thermodynamics, in isolated quantum systems. The goal of this research is to improve our understanding of the concept of thermal equilibrium in quantum systems. First, I investigated the role played by observables and measurements in the emergence of thermal behaviour. This led to a new notion of thermal equilibrium which is specific for a given observable, rather than for the whole state of the system. The equilibrium picture that emerges is a generalization of statistical mechanics in which we are not interested in the state of the system but only in the outcome of the measurement process. I investigated how this picture relates to one of the most promising approaches for the emergence of thermal behaviour in quantum systems: the Eigenstate Thermalization Hypothesis. Then, I applied the results to study the equilibrium properties of peculiar quantum systems, which are known to escape thermalization: the many-body localised systems. Despite the localization phenomenon, which prevents thermalization of subsystems, I was able to show that we can still use the predictions of statistical mechanics to describe the equilibrium of some observables. Moreover, the intuition developed in the process led me to propose an experimentally accessible way to unravel the interacting nature of many-body localised systems. Then, I exploited the "Concentration of Measure" and the related "Typicality Arguments" to study the macroscopic properties of the basis states in a tentative theory of quantum gravity: Loop Quantum Gravity. These techniques were previously used to explain why the thermal behaviour in quantum systems is such an ubiquitous phenomenon at the macroscopic scale. I focused on the local properties, their thermodynamic behaviour and interplay with the semiclassical limit. The ultimate goal of this line of research is to give a quantum description of a black hole which is consistent with the expected semiclassical behaviour. This was motivated by the necessity to understand, from a quantum gravity perspective, how and why an horizon exhibits thermal properties.

This dissertation defends the so-called 'agency-approach' to causation, which attempts to ground the causal relation in the cause's role of being a means to bring about its effect. The defence is confined to a conceptual interpretation of this theory, pertaining to the concept of causation as it appears in a causal judgement. However, causal judgements are not seen as limited to specific domains, and they are not exclusively attributed to human agents alone. As a methodological framework to describe the different perspectives of causal judgments, a method taken from the philosophy of information is made use of - the so-called 'method of abstraction'. According to this method, levels of abstraction are devised for the subjective perspective of the acting agent, for the agent as observer during the observation of other agents' actions, and for the agent that judges efficient causation. As a further piece of propaedeutic work, a class of similar (yet not agency-centred) approaches to causation is considered, and their modelling paradigms - Bayesian networks and interventions objectively construed - will be criticised. The dissertation then proceeds to the defence of the agency-approach, the first part of which is a defence against the objection of conceptual circularity, which holds that agency analyses causation in causal terms. While the circularity-objection is rebutted, I rely at that stage on a set of subjective concepts, i.e. concepts that are eligible to the description of the agent's own experience while performing actions. In order to give a further, positive corroboration of the agency-approach, an investigation into the natural origins and constraints of the concept of agency is made in the central chapter six of the dissertation. The thermodynamic account developed in that part affords a third-person perspective on actions, which has as its core element a cybernetic feedback cycle. At that point, the stage is set to analyse the relation between the first- and the third-person perspectives on actions previously assumed. A dual-aspect interpretation of the cybernetic-thermodynamic picture developed in chapter six will be directly applied to the levels of abstraction proposed earlier. The level of abstraction that underpins judgments of efficient causation, the kind of causation seemingly devoid of agency, will appear as a derived scheme produced by and dependent on the concept of agency. This account of efficient causation, the 'objectification of agency', affords the rebuttal of a second objection against the agency-approach, which claims that the approach is inappropriately anthropomorphic. The dissertation concludes with an account of single-case, or token level, causation, and with an examination of the impact of the causal concept on the validity of causal models.

Informationsthermodynamik ist der aktuelle Trend in der statistischen Physik. Es ist die theoretische Konstruktion eines einheitlichen Rahmens für die Beschreibung der Nichtgleichgewichtsmerkmale stochastischer dynamischer Systeme, wie die Dissipation der Arbeit und die Irreversibilität von Trajektorien, unter Verwendung der Sprache der Fluktuationstheoreme und der Informationstheorie. Die modellunabhängige Natur von Information und Irreversibilität ermöglicht eine breite Anwendbarkeit der Theorie auf allgemeinere (nichtphysikalische) Modelle aus der Systembiologie und der quantitativen Finanzmathematik, in denen asymmetrische Wechselwirkungen und Nichtlinearitäten allgegenwärtig sind. Insbesondere interessieren wir uns für Zeitreihe, die aus Messungen gewonnen werden oder aus einer Zeitdiskretisierung kontinuierlicher Modelle resultieren. In dieser Arbeit untersuchen wir die Irreversibilität von Zeitreihen unter Berücksichtigung der statistischen Eigenschaften ihrer Zeitumkehrung, und leiten daraus ein Fluktuationstheorem ab, das für Signal-Antwort-Modelle gilt, und das Irreversibilität sowie bedingte Informationen mit der Vergangenheit verknüpft. Interagierende Systeme tauschen kontinuierlich Informationen aus und beeinflussen sich gegenseitig. Intuitiv ist der kausale Einfluss der Effekt dieser Wechselwirkungen, der im Hinblick auf den Informationsfluss über die Zeit beobachtet werden kann, aber seine quantitative Definition wird in der Fachgemeinschaft immer noch diskutiert. Wir wenden insbesondere das Schema der partiellen Informationszerlegung (PID) an, das kürzlich definiert wurde, um synergistische und redundante Effekte aus informationstheoretischen Maßen zu entfernen. Hier schlagen wir unsere PID vor und diskutieren die resultierende Definition des kausalen Einflusses für den Sonderfall linearer Signal-Antwort-Modelle. / Information thermodynamics is the current trend in statistical physics. It is the theoretical research of a unified framework for the description of nonequilibrium features of stochastic dynamical systems like work dissipation and the irreversibility of trajectories, using the language of fluctuation theorems and information theory. The model-independent nature of information and irreversibility allows a wide applicability of the theory to more general (nonphysical) models from systems biology and quantitative finance, where asymmetric interactions and nonlinearities are ubiquitous. In particular, we are interested in time series obtained from measurements or resulting from a time discretization of continuous models. In this thesis we study the irreversibility of time series considering the statistical properties of their time-reversal, and we derive a fluctuation theorem that holds for time series of signal-response models, and that links irreversibility and conditional information towards past. Interacting systems continuously share information while influencing each other dynamics. Intuitively, the causal influence is the effect of those interactions observed in terms of information flow over time, but its quantitative definition is still under debate in the community. In particular, we adopt the scheme of partial information decomposition (PID), that was recently defined in the attempt to remove synergistic and redundant effects from information-theoretic measures. Here we propose our PID, and motivate the resulting definition of causal influence for the special case of linear signal-response models. The thermodynamic role of causal influences can only be discussed for time series of linear signal-response models in the continuous limit, and its generalization to general time series remains in our opinion the open problem in information thermodynamics.