This theoretical preprint develops a limited bridge from a specified two-state Hamiltonian with coherent coupling paths to a phase-dependent small-displacement stiffness. Reciprocal Ehrenfest forces and torque yield a conservative energy account; classical Langevin bath couplings and work-store or autonomous energy-depot controls extend the comparison to heat and supplied work. The autonomous free-depot branches have analytically determined rates that depend on the parameters. No independent selection of 0.218 Hz is obtained. A sustained mean rate and a shared phase are distinct, and the stochastic ensembles are independent repeats of one rotor, not a coupled rotor network. Illustrative scaled inputs are used throughout; physical Hz labels are conditional on a chosen reference time. The Born rule is an input. Material realization, global hybrid stability, full quantum Gibbs equilibrium and a complete Model-D embedding remain open. The package supplies the manuscript, source, figures, numerical records and integrity checks. No new empirical measurements or live Model-D integration are reported.
This theoretical preprint develops a limited bridge from a specified two-state Hamiltonian with coherent coupling paths to a phase-dependent small-displacement stiffness. Reciprocal Ehrenfest forces and torque yield a conservative energy account; classical Langevin bath couplings and work-store or autonomous energy-depot controls extend the comparison to heat and supplied work. The autonomous free-depot branches have analytically determined rates that depend on the parameters. No independent selection of 0.218 Hz is obtained. A sustained mean rate and a shared phase are distinct, and the stochastic ensembles are independent repeats of one rotor, not a coupled rotor network. Illustrative scaled inputs are used throughout; physical Hz labels are conditional on a chosen reference time. The Born rule is an input. Material realization, global hybrid stability, full quantum Gibbs equilibrium and a complete Model-D embedding remain open. The package supplies the manuscript, source, figures, numerical records and integrity checks. No new empirical measurements or live Model-D integration are reported.
A classical record can survive a quantum event, be read without demolition, and change later quantum dynamics. This work gives, under the displayed premises for each stage, a self-contained finite proof of the constructive chain from the first informative bit through one-, two-, and three-dimensional formation to an accessible 24-address classical fact, durable quantum-nondemolition record, operational clocks, and record-controlled quantum dynamics. The conjunction of finite formation, readable memory, native and noncommuting control, and a closed conditional regional solution is established here. The bridge maps are mathematically distinct, but their physical composition is conditional on those stage premises—including the adopted formation allocation and regional composition inputs—and on the parent event firing; the regional continuation uses the preserved completion statistic rather than the full fine address/facet record. An exact seven-branch Kraus intertwiner covers coherent inputs across 16,807 five-event histories, six physical lineages, and the complete no-event complement. The retained fine record controls a native repeat/comparison channel with hit probability eleven twenty-fifths, nonzero mutual information, and exact source-address independence, plus a noncommuting three-qubit response. A persistent occurrence projector autonomously enables a later instrument while preserving all admitted archive blocks. Worked continuations include an eight-write resource cycle, a record-preserving 16-cell consumer, and exact predictive compression. The conditional Fast-Time/Timescape continuation supplies an exact clock map, a closed scalar Buchert solution, an infinite connected shell-free Darmois collar family, and a positive-energy LRS completion family. Its approximately 88.2718196824 percent Hubble mismatch is a dependency-separated conditional kinematic diagnostic using an explicitly adopted measured matter fraction and derived radiation fiducial, with no dataset split or fitted parameter. It is not, by itself, an independent observational validation. No historical first claim or exhaustive classification is asserted; within the regional continuation, unique physical-member and optical-law selection remains open. Within those boundaries, the constructions establish a full-history bridge from the first distinction to durable fact, operational time, later quantum control, and an explicit closed conditional regional continuation.
Persistent control has to be realized by an interaction, with an error and a cost. We construct one such actuator: a degenerate bit coupled to a mode of a free chiral field through U=exp[−iλX(b+b†)] and a smooth switch g. For independent diagonal bit inputs, the same unitary fixes the flip error, added stress (g′)2/4, switching work λ2ωˉ and a positive quadratic cost on switch profiles. A flip with failure ϵ needs mean drive occupation at least θϵ(1−2ϵ)/[4ϵ(1−ϵ)]−21, where θϵ=arccos(2ϵ−1); the leading cost is π/(4ϵ). Displaced squeezed states nearly attain it, whereas classical drives need order ϵ−1. A calibrated feedback task with scheduled fresh independent drives has an exact stationary loss, coupling rate and stability proof, with one acceptance condition joining calibration records to drive energy. A second bound prices response readout: if two branches differ only by probe delays bounded in difference by Δτ, binary error ϵ requires EΔτ≥ℏ[1−2ϵ(1−ϵ)]/ζ, with ζ=maxx>0(1−cosx)/x. Retained ancillas and joint decoding do not remove this bound, and a three-level construction saturates it across the allowed signed-delay families. A retained oscillator also supports a thermal branch: a coherent echo protects held quantum content, a mixed qubit port reads the coupling through one binary outcome, and a finite Gibbs bank restores the oscillator while retaining every spent output. These energy and memory accounts do not identify exported energy with removed entropy. The descent metric, physical work form and Lorentzian propagation form remain distinct.
We present the dataset and comprehensive manuscripts for the TROIKA (Triple Rotor Oscillator Interlinked with K-cycle Architecture) model. This framework establishes a bridge between discrete geometric entanglement and continuous rotational mechanics, exploring the hybrid coupling between directional degrees of freedom and continuous vibrational modes across three entangled sources. The provided documentation includes the full theoretical derivation of a cyclically entangled three-qutrit state that enforces a strict orthogonal trihedron upon projective measurement. By utilizing Weyl-Heisenberg shift operators and establishing a discrete phase variable through a classical Lagrangian, the model derives a novel directional-vibrational interaction Hamiltonian. Additionally, the full manuscripts detail the exact global symmetry operator (K) that confines the system's dynamics within an invariant subspace, drastically reducing the active Hilbert space dimensionality. Furthermore, this deposit includes the complete suite of MATLAB source codes used to solve the time-independent Schrödinger equation via exact matrix diagonalization and Kronecker products. The codebase implements advanced matrix contractions to compute partial traces, tracking non-Markovian Rabi revivals, Von Neumann entanglement entropy, and Wigner quasiprobability distributions—formally demonstrating the active generation of non-classical vibrational states with distinct negativity wells in phase space. Finally, an open-ended continuous extension is formulated, showcasing the discrete cyclic structure as an effective low-energy sector of an isotropic rigid rotor on the SO(3) configuration manifold. Files included:- Theoretical Manuscript in English (PDF)- Theoretical Manuscript in Spanish (PDF)- Core MATLAB source codes for dynamics, entropy, and Wigner functions (.m)
We investigate the thermodynamics of a hybrid quantum device consisting of two qubits collectively interacting with a quantum rotor and coupled dissipatively to two equilibrium reservoirs at different temperatures. By modeling the dynamics and the resulting steady state of the system using a collision model, we identify the functioning of the device as a thermal engine, a refrigerator, or an accelerator. In addition, we also look into the device's capacity to operate as a heat rectifier and optimize both the rectification coefficient and the heat flow simultaneously. Drawing an analogy to heat rectification and since we are interested in the conversion of energy into the rotor's kinetic energy, we introduce the concept of angular momentum rectification, which may be employed to control work extraction through an external load.
Traditional quantum thermodynamic frameworks associate work to energy exchanges induced by unitary transformations generated by external controls, and heat to energy exchanges induced by bath interaction. Recently, a framework was introduced aiming at extending the thermodynamic formalism to genuine quantum settings, also referred to as autonomous quantum systems: free from external controls, only quantum systems interacting with each other. In this paper, we apply such a thermodynamic framework to common experimental situations of interacting quantum systems. In situations where traditional frameworks detect only heat exchanges, the recent autonomous thermodynamic framework points at work exchanges based on two mechanisms: population inversion and coherence generation / consumption. Such mechanisms are well known in the literature for being related to work expenditure and extraction, in particular in relation with ergotropy, which emphasizes the relevance of the autonomous framework and the limitations of traditional ones. Furthermore, the autonomous framework also identifies a genuine non-unitary mechanism of work exchange related to athermality. %, also pointed out as a resource for work extraction. Finally, in the semi-classical limit, the autonomous framework identifies all energy exchanges as pure work, but distinguishes between local work and interaction energy.
Our results show that the autonomous framework provides a refined analysis of work exchange mechanisms in the quantum realm and serves as a consistent approach to analyze thermodynamic processes in realistic quantum devices.
This monograph develops the Shadow Theory quantum measurement programme through two distinct physical constitutions, connecting source dynamics to actual events, Born-rule measurement statistics, material records and subsequent measurements. The pilot-medium construction combines canonical current production, conservative packet export, independently prepared deterministic gas contacts, finite recombination and carrier-population tracking. Under its stated assumptions, the complete ordinary tagged path converges in total variation to the minimal Bell process in unchanged physical time. An autonomous finite-clock construction supplies faithful first-pass records, retained resources and noncommuting continuation. The separate massive-configuration construction adopts Bohmian guidance and complete initial quantum equilibrium. It supplies explicit material detectors, archives, reset operations and autonomous control, with separate bounds for retained outputs and historical record fidelity. The volume integrates proofs, counterexamples and the programme’s detector, preparation and protection results. It presents conditional internal completions within declared premises, rather than a derivation of those premises from source/readout incompleteness. The pilot result is a controlled effective limit; the massive result is a separate operational completion. This preprint is offered for independent scrutiny.