Abstract:Building upon the analytic quantum thermodynamic framework I previously established (Zou, 2025), this article presents a discrete ontological model in which the arrow of time emerges from irreversible energy transfers driven by local energy gradients on a topologically fixed spatial network, with the temporal sequence identified as the successive updates of spatial energy redistribution. A multiplicative entropy, defined as the product of all node energies, increases exactly with every transfer, providing a non-statistical, step-by-step measure of temporal progression. I argue that energy dissipation is fundamentally identical to decoherence: the former supplies the physical mechanism, the latter the observational signature. This framework synthesizes three intellectual traditions—computational time (Wolfram, 't Hooft), gradient-driven thermodynamics (Annila), and decoherence (Joos & Zeh, Kiefer)—into a unified picture where time is the counting of irreversible energy redistribution on discrete space.
Abstract:Building upon the analytic quantum thermodynamic framework I previously established (Zou, 2025), this article presents a discrete ontological model in which the arrow of time emerges from irreversible energy transfers driven by local energy gradients on a topologically fixed spatial network, with the temporal sequence identified as the successive updates of spatial energy redistribution. A multiplicative entropy, defined as the product of all node energies, increases exactly with every transfer, providing a non-statistical, step-by-step measure of temporal progression. I argue that energy dissipation is fundamentally identical to decoherence: the former supplies the physical mechanism, the latter the observational signature. This framework synthesizes three intellectual traditions—computational time (Wolfram, 't Hooft), gradient-driven thermodynamics (Annila), and decoherence (Joos & Zeh, Kiefer)—into a unified picture where time is the counting of irreversible energy redistribution on discrete space.
This report synthesizes a definitive paradigm shift in quantum thermodynamics, formalizing the proposition that the thermodynamic arrow of time is not a global inevitability but a localized, structurally dependent, and mathematically malleable vector that can be actively engineered at the microscopic scale. This is achieved by analyzing the architecture of irreversibility through the rigorous mathematical lens of information geometry. Quantum states are represented as coordinates on a statistical manifold equipped with Petz monotone metrics (like the Bures-Helstrom metric). Within this framework, thermodynamic irreversibility and the arrow of time emerge as precisely defined geometric flows. The core thesis is that the arrow of time is the natural gradient flow of information-theoretic entropy (Rényi entropy) along the geodesics of the quantum statistical manifold. The report details three primary methods for active manipulation: (1) Active reversal using continuous measurement and Feedback Hamiltonians, which function as the exact score function of the quantum trajectory distribution to steer states against the natural entropy gradient. (2) Decentralizing the arrow of time by defining it as a local vector field subordinate to Quantum Causal Influence (QCI), which explains phenomena like coexisting and periodically inverting temporal directions in quantum many-body scars. Also available on Academia.edu: https://www.academia.edu/attachments/132724601/download_file?s=portfolio
AbstractThe origin of the arrow of time—why entropy always increases, why we can only remember the past—is one of the deepest puzzles in physics. Boltzmann’s statistical explanation attributes entropy increase to a low-entropy “past hypothesis,” but it does not explain the origin of this initial condition itself. Landauer’s principle reveals a quantitative connection between information erasure and heat dissipation, yet it does not answer why information erasure is fundamentally irreversible. This paper proposes a unified solution within the two-phase information conservation framework: the arrow of time is the macroscopic statistical manifestation of the irreversibility of information settlement between the material phase (Ξ) and the information phase (Ω). Each information settlement event simultaneously produces four outcomes: formation of an information record, local collapse of the material phase state, update of observer coherence parameters, and consumption of dark energy accompanied by heat release. Once settlement is completed, it cannot be undone; the unidirectional flow of time is precisely the macroscopic bookkeeping of this settlement irreversibility. Starting from the principle of least action incorporating two-phase coupling, we provide a rigorous proof that the settlement process is not invariant under time reversal, and derive a quantitative relation between the entropy production rate and the macroscopic information activity rate. This framework unifies the thermodynamic arrow, the quantum measurement arrow, the decoherence arrow, and the cosmological arrow as manifestations of the same settlement process at different scales, offering a natural explanation for the past hypothesis and the entanglement past hypothesis. We present three testable predictions: a weak dependence of the CHSH violation parameter on the measurement time difference in Bell experiments, a scaling relation between decoherence rate and information-phase coupling strength at ultra-low temperatures, and the gravitational memory effect as a cumulative signature of settlement records on cosmological scales. This work unifies the arrow of time with quantum measurement, black hole information processing, dark energy cosmology, quantum entanglement, the Higgs mechanism, and the third law of thermodynamics under a single cross-scale information settlement paradigm.Keywords: arrow of time, second law of thermodynamics, Landauer’s principle, information settlement, irreversibility, entropy increase, time-reversal symmetry breaking, gravitational memory effect, past hypothesis
Abstract The ontological status of time remains unresolved in fundamental physics. In quantum mechanics, time appears as an external classical parameter, whereas in general relativity it is dynamical and intertwined with spacetime geometry. Canonical approaches to quantum gravity, most notably the Wheeler–DeWitt formulation, eliminate time altogether, leading to the well-known “problem of time.” These tensions motivate frameworks in which time is not fundamental but emergent. In this work, we propose a discrete, update-based framework in which the universe evolves through a sequence of global quantum states indexed by an abstract update parameter rather than by a physical time coordinate. Evolution is formulated as a completely positive, trace-preserving (CPTP) quantum channel acting on the universal density operator, ensuring exact conservation of probability and global quantum information at every update. The framework is deliberately conservative: it preserves the formal structure of quantum mechanics and quantum field theory, enforces vacuum stability, and supports global conservation laws without introducing new dynamical postulates. Within this setting, time emerges relationally at the level of subsystems. As subsystems become increasingly entangled with their environments, entropy gradients arise that define an effective arrow of time, closely aligned with the thermodynamic arrow. The resulting temporal flow is relative, statistical, and observer-dependent, while the global evolution remains information-preserving and, in the closed-system limit, reversible. We explore the implications of this framework for cosmology and black hole physics. The Big Bang is reinterpreted as an initial quantum state rather than a singular beginning of time, avoiding temporal singularities. Black hole evaporation is shown to be compatible with unitary evolution when the full quantum state is considered, naturally reproducing the expected Page curve and resolving the apparent information paradox. Overall, the framework provides a coherent, minimal setting in which time, irreversibility, and cosmological history emerge from quantum correlations rather than from a fundamental temporal background.
We extend Barandes’ indivisible stochastic interpretation of quantum mechanics to address the emergence of classical spacetime and the arrow of time from collective quantum processes. While Barandes (2025) demonstrates that individual quantum sys- tems can be understood as indivisible stochastic processes, we show that when many such systems interact, their collective behavior generates emergent spatial structure through quantum correlations and emergent temporal divisibility through thermody- namic irreversibility. Specifically, we argue that: (1) spatial relations emerge from patterns of quantum entanglement and correlation among multiple actualizations; (2) thermodynamic entropy production in many-body systems creates an irreversible ar- row of time; (3) this irreversibility transforms the fundamentally indivisible quantum process into an apparently divisible classical process; and (4) the time parameter t itself emerges as a bookkeeping device for tracking these irreversible collective changes. This framework provides a unified account of the quantum-to-classical transition, connect- ing quantum foundations, statistical mechanics, and emergent spacetime in a coherent picture where both space and time arise from the collective dynamics of indivisible quantum actualizations.
We propose a speculative but quantitatively constrained phenomenological framework in which the thermodynamic arrow of time emerges from entropy-dependent decoherence in open quantum systems. Higher environmental entropy strengthens decoherence, preferentially de- stroying quantum coherence in one temporal direction, thus providing a microscopic mechanism for irreversibility. The formalism is constructed within an effective Lindblad master-equation approach, recovering unitary quantum mechanics and standard thermodynamics in appropriate limits. A toy two-level system illustrates the emergence of coherence decay and an effective microscopic arrow of time.
The concept of time presents a profound challenge at the intersection of quantum mechanics and thermodynamics. While fundamental microscopic laws are largely time-symmetric, macroscopic phenomena universally exhibit a distinct thermodynamic arrow of time, characterized by increasing entropy. This paper explores the hypothesis that quantum entanglement plays a crucial role in the emergence of this thermodynamic arrow. We review how the entanglement between a quantum system and its environment leads to decoherence, effectively driving the system towards a state of higher entropy and classical-like behavior. By analyzing concepts such as von Neumann entropy, entanglement entropy, and the Page-Wootters mechanism, we propose a theoretical framework where the degradation and spreading of entanglement act as the underlying mechanism for the perceived unidirectional flow of time. This approach offers a potential resolution to the "problem of time" in quantum gravity and provides a unified perspective on the genesis of irreversibility from the inherently reversible laws of quantum mechanics. We discuss the implications of this entanglement-driven temporal emergence for our understanding of the universe's initial low-entropy state and the fundamental nature of reality.