One of the major unsolved problems in physics is the contradiction betwee n the reversibility of the microscopic world, as described by quantum mech anics, and the irreversibility of the macroscopic world, as described by c lassical thermodynamics and statistical mechanics.Specifically, time evol ution governed by the Schrödinger equation is unitary and possesses time-r eversal symmetry, and the von Neumann entropy of a microscopic system is c onserved.However, the entropy increase observed in macroscopic, isolated systems according to the second law of thermodynamics cannot be explained by unitary time evolution and von Neumann entropy alone.This doctoral dissertation presents a unified framework that uses observe rs to explain the contradiction.Based on von Neumann's concept of macrosc opic entropy, the framework redefines these concepts through the lens of q uantum information theory and specifically, Petz's theory of quantum suffi ciency and resource theory.This research proposes that macroscopic irreversible phenomena do not vio late physical laws.Instead, these phenomena result from the loss of stati stical information caused by limitations in an observer's measurement capa bilities or by coarsening.This doctoral thesis specifically focuses on ob servational entropy, which is a generalization of von Neumann's macroscopi c entropy.Chapter 4 of this study reinterprets von Neumann's H-theorem within a con temporary framework.The chapter provides a mathematical proof of the irre versible increase of observational entropy in isolated quantum systems.It was demonstrated that, when the system's initial state is macroscopic, or lacking microscopic details with respect to a specific measurement, obser Macroscopic States, Operations, and Entropy: An Obser ver-Centric Approach (巨視的な状態、操作、エントロピー ：観測者中心のアプローチ) 長澤 輝明
It is often claimed that the fundamental laws of physics are deterministic and time-symmetric and that therefore our experience of the passage of time is an illusion. This paper will critically discuss these claims and show that they are based on the misconception that the laws of physics are an exact and complete description of nature. I will argue that all supposedly fundamental deterministic and time-symmetric laws have their limitations and are supplemented by stochastic and irreversible elements. In fact, a deterministic description of a system is valid only as long as interactions with the rest of the world can be ignored. The most famous example is the quantum measurement process that occurs when a quantum system interacts with a macroscopic environment such as a measurement apparatus. This environment determines in a top-down way the possible outcomes of the measurement and their probabilities. I will argue that more generally the possible events that can occur in a system and their probabilities are the result of top-down influences from the wider context. In this way the microscopic level of a system is causally open to influences from the macroscopic environment. In conclusion, indeterminism and irreversibility are the result of a system being embedded in a wider context.
Quantum mechanics is widely recognised as being incomplete. It is not consistent with the second law of thermodynamics and does not provide a scientifically credible physical account of the measurement process, the means by which coherence is broken and classically observable states are recorded. This has led to many ad hoc assumptions being used to account for various properties of quantum systems, among which is the coherence time of quantum devices that determines their ability to perform computations. Here, we show that all these properties can be accommodated naturally and consistently in the context of mixing quantum systems which exhibit continuous spectra, as arises in the thermodynamic limit in quantum statistical mechanics and quantum gravity. In particular, for isolated systems we show that the time-reversal symmetry associated with unitary time evolution of the quantum state gives rise to time-symmetry breaking and a semi-group evolution which attains thermodynamic equilibrium at long times. Moreover, the emergence of this non-unitary time-asymmetry leads to microcanonical equilibrium states in which all quantum coherence is lost and is accompanied by the transformation of pure states into mixtures, leading in turn to an increase in entropy. Inclusion of a macroscopic measurement apparatus shows how the outcome of a measurement corresponds to the von Neumann projection postulate, arising with probabilities in conformance with the Born rule. The mathematical structure of the theory which applies to quantum systems with continuous spectra is closely analogous to the classical ergodic theory of dynamical systems and the conditions under which they attain equilibrium states.
Since the mechanism of spontaneous symmetry breaking has such a relevant impact for the description of physical systems, its explanation should be based on physical considerations with a direct operational meaning. To this purpose, it is useful to recognize that the operational/experimental description of a physical system (not necessarily quantum!) involves the following elements: the set A of its measurable quantities, briefly called observables ; the measurement of the time evolution of the observables; the set ∑ of configurations or states in which the system may be prepared, according to well defined protocols of experimental preparations; the measurement of an observable A , when the system is in the state ω is operationally defined by the experimental expectation 〈A〉 ω
We present a unified operational framework for the arrow of time grounded in irreversible information loss. While microscopic physical laws are time-reversal invariant, macroscopic irreversibility arises when systems overwrite metastable records. We show that recent reversible quantum-control experiments do not reverse time, but instead operate in regimes where no logically irreversible record is created. To formalize this, we introduce the **forgetting rate**
(Ξcr), a coarse-grained rate defined on physically selected metastable record states (e.g., pointer states, memory registers, or macroscopic configurations). Unlike standard entropy production, which is expressed in terms of microscopic transition asymmetry,
(Ξcr) captures the **rate of irreversible record overwriting**. In this formulation, entropy production obeys the lower bound
S˙irr≥kBΞcr,consistent with Landauer's principle but expressed at the level of record dynamics. Within this framework, thermodynamic, quantum-measurement, psychological, and cosmological arrows emerge as substrate-dependent manifestations of
Ξcr>0. Temporal asymmetry is therefore not a single global property, but a distributed feature of physical information-processing systems. The approach naturally explains the decoupling of arrows in composite systems and identifies experimentally accessible regimes where irreversibility can be locally suppressed. This work does not introduce a new microscopic law but provides a unifying, operational reformulation that connects information thermodynamics, decoherence theory, and memory dynamics through a single coarse-grained rate.