This volume transitions the quantum thermodynamics discourse from merely observing macroscopic irreversibility to its active creation, manipulation, and structural engineering at the microscopic scale. The theoretical foundation is established by anchoring the universal arrow in the Entanglement Past Hypothesis (EPH), which posits a pure, unentangled initial state for the universe, and the "tooth of time" mechanism, which links irreversibility to state-space non-degeneracy. The paper demonstrates that the thermodynamic arrow is a highly local and malleable resource, governed not by a monolithic global time parameter, but by the geometric flow of Quantum Causal Influence (QCI) and local Rényi entropy gradients. This is evidenced by spontaneous temporal oscillations observed in constrained non-ergodic systems like quantum many-body scars. Operationally, the arrow can be inverted locally by using continuous measurement back-action and targeted feedback Hamiltonians, enabling quantum engines to extract coherent work and drive processes like spontaneous cold-to-hot heat flow by leveraging initial quantum correlations. Furthermore, the Intrinsic Hamiltonian of Mean Force (I-HMF) is introduced to rigorously secure the equivalence between information loss and physical irreversibility even in the extreme strong-coupling regime. Also available on Academia.edu: https://www.academia.edu/attachments/132724386/download_file?s=portfolio
This volume transitions the quantum thermodynamics discourse from merely observing macroscopic irreversibility to its active creation, manipulation, and structural engineering at the microscopic scale. The theoretical foundation is established by anchoring the universal arrow in the Entanglement Past Hypothesis (EPH), which posits a pure, unentangled initial state for the universe, and the "tooth of time" mechanism, which links irreversibility to state-space non-degeneracy. The paper demonstrates that the thermodynamic arrow is a highly local and malleable resource, governed not by a monolithic global time parameter, but by the geometric flow of Quantum Causal Influence (QCI) and local Rényi entropy gradients. This is evidenced by spontaneous temporal oscillations observed in constrained non-ergodic systems like quantum many-body scars. Operationally, the arrow can be inverted locally by using continuous measurement back-action and targeted feedback Hamiltonians, enabling quantum engines to extract coherent work and drive processes like spontaneous cold-to-hot heat flow by leveraging initial quantum correlations. Furthermore, the Intrinsic Hamiltonian of Mean Force (I-HMF) is introduced to rigorously secure the equivalence between information loss and physical irreversibility even in the extreme strong-coupling regime. Also available on Academia.edu: https://www.academia.edu/attachments/132724386/download_file?s=portfolio
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
The problem of time’s arrow is (roughly) to understand why macroscopic physical processes typically evolve in a specific direction (the one we call “the future”) even though the underlying laws of physics describing the individual microscopic systems are time-reversal invariant. The standard answer to this problem is given by Boltzmann’s explanation of the II law of thermodynamics: a classical system starting in a non-equilibrium state spontaneously (i.e. with a high level of probability) tends towards equilibrium, thus implementing an irreversible process. However, this explanation has two drawbacks: 1. it needs a further assumption on the entropy of the initial state of the universe (past hypothesis); 2. microscopic systems (e.g. molecules in a box) should be represented as quantum states and not classical states. In this talk, I want to propose a different hypothesis to explain the origin of time’s arrow, based on quantum mechanics, specifically on decoherence theory. Differently from isolated systems, open quantum systems described by decoherence theory showirreversible behavior, as they evolve towards decoherence and von Neumann entropy increase. Is this behavior a sign of genuine irreversibility? And, if so, can this be linked to thermodynamic irreversibility?
This work investigates the fundamental connection between quantum mechanics and thermodynamics through the concept of the arrow of time. While the second law of thermodynamics identifies the arrow of time with the monotonic increase of entropy in isolated systems, closed quantum systems evolve unitarily and conserve von Neumann entropy, making the origin of irreversibility less apparent. Here we establish a no-go theorem proving that correlations in unknown states of closed quantum systems cannot be universally removed by any physical operation. This result demonstrates that correlation generation is inherently irreversible, providing a microscopic and universal basis for the arrow of time. In thermodynamic settings, this irreversibility ensures that heat flows spontaneously from hotter to colder subsystems, reproducing the Clausius formulation of the second law. More generally, the irreversible growth of correlations explains entropy increase, the approach to equilibrium, and decoherence as observable manifestations of the same principle. Our findings ground a quantum-mechanical foundation for the second law of thermodynamics and demonstrate the universality of the arrow of time.
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
This report constructs a rigorous theoretical bridge connecting the deterministic evolution of isolated quantum systems, governed by the Hamiltonian operator, with the irreversible, macroscopic thermalization demanded by the second law of thermodynamics. It utilizes the Eigenstate Thermalization Hypothesis (ETH) to reconcile this contradiction, asserting that individual energy eigenstates are intrinsically thermal. To transcend ETH's descriptive limits, the Statistical Jacobi Approximation (SJA) is introduced to predict far-from-equilibrium dynamics and response functions following quantum quenches without requiring complete re-diagonalization. The document demonstrates that multiscale energy transfer, specifically the inverse energy cascade mediated by recursive zig-zag patterns observed in classical turbulence, persists within microscopic quantum superfluids and optical lattices. Critically, to stress-test these frameworks, the report employs fractal geometries as advanced simulational incubators. Fractals, by Mamun, SM (2026) ………………………….1 Quantum Mechanics, the Hamiltonian, and Thermodynamics: Predicting Eigenstates via Fractal Simulations (Volume II) K S C breaking translational symmetry, lead to the emergence of non-ergodic multifractal (NEM) states that actively defy ETH, and provide empirical validation through the high-resolution observation of Hofstadter's Butterfly in moiré superlattices. Also available on Academia.edu: https://www.academia.edu/attachments/132683179/download_file?s=portfolio
The origin of the macroscopic arrow of time remains one of the most profound puzzles in theoretical physics, traditionally tied to the monotonic increase of total entropy dictated by the second law of thermodynamics. In this work, we propose and rigorously analyze the concept of the Quantum Thermodynamic Arrow Inverter (QTAI), a theoretical framework designed within open quantum systems where a local subsystem can exhibit a transient or sustained decrease in local entropy, characterized mathematically by d S_sub / dt < 0, while the global composite system strictly satisfies the global second law of thermodynamics, given by d S_total / dt >= 0. Rather than focusing merely on conventional cooling or refrigeration cycles, QTAI investigates whether the thermodynamic arrow of time can be dynamically and non-trivially redistributed across entangled and correlated quantum sub-degrees of freedom. By leveraging non-Markovian system-environment interactions, quantum coherence, and information-theoretic resource allocation, we demonstrate that different subsystems can effectively experience distinct local temporal directions or asymmetric thermodynamic aging. This paradigm introduces the Arrow of Time Redistribution as a fundamental principle, potentially bridging quantum information theory, open system dynamics, and the foundational nature of time itself.