The contradiction between the thermodynamic arrow of time and microscopic dynamical reversibility is a core problem in statistical physics. Within the framework of connectivity engineering, this paper proposes a new mechanism: irreversible accumulation of subsystem entropy caused by topological quenching. We numerically simulate the cyclic switching of a one-dimensional spin network between topological steps k=1 and k=4. Results show that each switch from the highly connected state to the frustrated state leads to an irreversible "fall" of information into the local entanglement space; when switched back to the initial topology, the subsystem entanglement entropy cannot recover to its initial value, but instead surges from 0 to approximately 2.96 and remains in the saturation regime, exhibiting a unidirectional entropy accumulation. Since the theoretical maximum entropy of this subsystem is 3.0, this irreversible saturation directly reveals the limit of information coarse-graining. The above results prove that the microscopic origin of the arrow of time is precisely the information scrambling caused by the irreversibility of underlying geometric topological reconstruction.
The contradiction between the thermodynamic arrow of time and microscopic dynamical reversibility is a core problem in statistical physics. Within the framework of connectivity engineering, this paper proposes a new mechanism: irreversible accumulation of subsystem entropy caused by topological quenching. We numerically simulate the cyclic switching of a one-dimensional spin network between topological steps k=1 and k=4. Results show that each switch from the highly connected state to the frustrated state leads to an irreversible "fall" of information into the local entanglement space; when switched back to the initial topology, the subsystem entanglement entropy cannot recover to its initial value, but instead surges from 0 to approximately 2.96 and remains in the saturation regime, exhibiting a unidirectional entropy accumulation. Since the theoretical maximum entropy of this subsystem is 3.0, this irreversible saturation directly reveals the limit of information coarse-graining. The above results prove that the microscopic origin of the arrow of time is precisely the information scrambling caused by the irreversibility of underlying geometric topological reconstruction.
In the framework of connectivity engineering, this paper proposes a method to inversely reconstruct the internal discrete topological connectivity from the boundary entanglement entropy spectrum. Based on a one-dimensional spin-1/2 network, we extract a three-dimensional entanglement fingerprint characterizing the internal connectivity: the mutual information peak, the peak position, and the late-time residual fidelity. Numerical diagnostics show that when the connectivity reaches k=3, the mutual information peak reaches 1.49 times that of the baseline network, and the system enters the topological saturation regime; at this point, the fingerprint vectors for k=3 and k=4 are indistinguishable within numerical precision. We prove that this degeneracy originates from the joint mechanism of graph-theoretic topology and dynamical decay, and further increasing k does not yield substantial cross-region entanglement channels. Even in the presence of numerical noise, the significant gap in late-time fidelity between k=2 and the saturation regime ensures the high robustness of the inverse mapping. This result establishes the effectiveness of the "entanglement fingerprint distance" as an inverse diagnostic operator, providing an operational benchmark for discrete bulk geometry reconstruction using purely boundary observables.
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
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 boundS˙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.
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.
There is a huge discrepancy between the divergent vacuum zero-point energy in quantum field theory and the macroscopic cosmological constant. Within the framework of connectivity engineering, this paper explores the regulatory mechanism of underlying graph topology on the ground state energy of finite systems. By introducing a truncated step k in a one-dimensional XXZ spin network, numerical results show that the absolute value of the system's ground state energy does not decline trivially and linearly with the reduction of interaction bonds, but rather exhibits strong non-trivial topological frustration. The normal network (k=1), due to strong local entanglement, exhibits a lower bare ground state energy density; while after introducing long-range geometric decoupling, the parity matching of sub-chain lengths and boundary reconstruction lead to a non-monotonic evolution of the ground state energy density, reaching a maximum at k=4 due to odd-lattice frustration. This topology-induced energy renormalization conceptually provides a minimal discrete sandbox for the "geometric truncation" of vacuum energy, and implies that the residual energy of macroscopic spacetime (dark energy) may correspond to the geometric frustration tension of the underlying discrete network that has not been fully canceled after topological saturation.