In this paper, we propose and formalize the concept of Energy-Information Phase Locking (EIPL), addressing the fundamental question of whether information flow possesses an independent dynamical phase capable of synchronizing with energy flow in open quantum systems. By introducing complex field representations for both energy currents and information transfer rates, we establish the core phase difference observable Phi_EI(t) = phi_E(t) - phi_I(t). We derive the governing nonlinear equations of motion, demonstrating that under specific non-equilibrium conditions, the phase difference stabilizes to a constant locking value Phi_0 when intrinsic frequency mismatches are bounded by cross-coupling strengths. Furthermore, we analyze the thermodynamic implications of EIPL, showing how persistent phase cross-correlations modify standard entropy production bounds and fluctuation theorems. This theoretical framework bridges quantum thermodynamics and information theory, offering new insights into phase-coherent energy dissipation and optimal information processing in quantum technologies.
In this paper, we propose and formalize the concept of Energy-Information Phase Locking (EIPL), addressing the fundamental question of whether information flow possesses an independent dynamical phase capable of synchronizing with energy flow in open quantum systems. By introducing complex field representations for both energy currents and information transfer rates, we establish the core phase difference observable Phi_EI(t) = phi_E(t) - phi_I(t). We derive the governing nonlinear equations of motion, demonstrating that under specific non-equilibrium conditions, the phase difference stabilizes to a constant locking value Phi_0 when intrinsic frequency mismatches are bounded by cross-coupling strengths. Furthermore, we analyze the thermodynamic implications of EIPL, showing how persistent phase cross-correlations modify standard entropy production bounds and fluctuation theorems. This theoretical framework bridges quantum thermodynamics and information theory, offering new insights into phase-coherent energy dissipation and optimal information processing in quantum technologies.
A central open question in quantum thermodynamics is the identification of thermodynamic entropy away from equilibrium. Although thermodynamic entropy coincides with the von Neumann entropy for a Gibbs state at equilibrium, the thermodynamic role of quantum coherence generated during nonequilibrium evolution remains unclear. Here, we show that von Neumann entropy does not, in general, represent the thermodynamic entropy governing heat exchange in coherent nonequilibrium quantum systems. By integrating the resource theory of quantum coherence with thermodynamic principles, we develop a general framework for nonequilibrium quantum thermodynamics. We identify thermodynamic entropy with the energy entropy derived from energy-measurement statistics and introduce a dynamical temperature extending the equilibrium concept to nonequilibrium states. Consequently, we obtain an exact entropy-balance relation separating the entropy flux associated with heat exchange from the coherence-loss contribution to entropy production, establishing an operational connection between quantum coherence, heat flow, and total entropy change. Unlike approaches relying on equilibrium reference states or stationary Gibbs ensembles, our framework uses instantaneous dynamical quantities and remains valid throughout transient nonequilibrium evolution. It provides consistent dynamical definitions of temperature, work, heat, and free energy. Applying the formalism to an exactly solvable open quantum system, we show that the first and second laws hold throughout transient evolution and that equilibrium thermodynamics emerges dynamically in the weak-coupling long-time limit. Our results establish a unified framework for coherent nonequilibrium quantum thermodynamics and suggest opportunities for controlling heat dissipation through coherence engineering in quantum thermal technologies.
Modern quantum theory offers powerful insights into superposition, entanglement, and decoherence, yet lacks a unifying treatment of information flow, observer participation, and entropy stability within dynamical systems. In this work, we introduce a novel framework based on \textit{probabilistic tensor fields}-a formulation in which quantum evolution, informational geometry, and observer-phase interaction co-emerge from a unified structure. The system is described by a dynamic field Ψμν, composed of a coherent geometric background ⟨Gμν⟩ and a fluctuating informational term σμν. The observer is embedded as a phase function ϕobserver, dynamically interacting with the field to generate localized coherence.This coupling induces entropy suppression, spontaneous convergence (measurement), and classical pattern emergence-without invoking wavefunction collapse. Simulations reveal field-phase locking, entropy decay, vacuum energy damping, and the formation of stable memory attractors through standing-wave coherence. These results provide a new perspective on the quantum-to-classical transition, suggest a field-based alternative to gate-based computation, and offer a mathematically consistent path toward entropy-regulated dynamics. Recent experimental platforms support programmable phase dynamics and coherence engineering \cite{Bloch2008, Indiveri2015}, enabling physical analogs to IOQD simulations. Thereby, we position IOQD as a coherence-driven, phase-adaptive field computation model extending quantum machine learning beyond variational circuits and gate-based logic into non-symbolic, dynamic attractor learning systems.
The intersection of information theory and fundamental physics has traditionally centered on the thermodynamic cost of computation, entropy bounds, and the informational interpretation of quantum states. This paper introduces the theoretical framework of Negative Information Pressure (NIP), positing that high-density quantum information structures exert an effective mechanical and thermodynamic force analogous to pressure. By defining an information energy term proportional to the quantum information complexity of a system, denoted as E_I = \lambda * I(\rho), we derive an explicit formulation for negative information pressure as the negative partial derivative of information energy with respect to system volume, P_I = -(\partial E_I) / (\partial V). This framework bridges the conceptual gap between abstract information configurations and concrete physical dynamics, suggesting that highly compressed, entangled, or structured quantum states can actively modify local boundary responses and macroscopic forces without requiring classical particle interactions. The implications of this paradigm extend the foundational motto of information physics into a dynamic realm where information directly governs physical evolution, offering new theoretical perspectives for quantum thermodynamics and information-driven physical systems.
In this paper, we introduce the concept of the Quantum Energy-Time Lattice (QETL), a theoretical framework proposing that discrete energy exchange events in non-equilibrium open quantum systems can naturally form a structured lattice in the temporal and energetic domains. Unlike conventional discrete time crystals that break continuous time-translation symmetry through periodic driving of spatial or spin configurations, the QETL framework posits that periodicity emerges intrinsically within the energy exchange profile such that E(t + nT_E) equals E(t), where T_E represents the fundamental energy-exchange period and n is an integer. Crucially, we demonstrate that a system exhibiting this temporal-energetic lattice structure does not necessarily manifest as an ordinary time crystal, as the underlying quantum state may retain internal phase fluctuations or decoherence channels that prevent standard sub-harmonic synchronization. We formulate the mathematical dynamics governing QETL, analyze its characteristic observable signals where the energy exchange spectrum exhibits sharp peaks at omega_n equal to nomega_E, and explore the profound implications of establishing a dual energy-time lattice symmetry. This paradigm opens new avenues for exploring non-equilibrium quantum matter and offers deep insights into the fundamental interplay between energy dissipation, temporal order, and quantum coherence.
Synchronization is a collective phenomenon in which interacting nonlinear oscillators develop a persistent relation between their phases and frequencies. In quantum systems, its description requires connecting the classical dynamics of limit-cycle oscillators with quantum fluctuations, dissipation, and the notion of phase. In this tutorial review, we offer a systematic framework for analyzing synchronization in classical and quantum dynamical systems. Starting from amplitude-phase dynamics, we introduce successively topics of relevance, such as phase locking, the Adler equation, Arnold tongues, and the Kuramoto model, and use these concepts to analyze coupled oscillators and their stability. We then formulate the corresponding description for quantum limit-cycle oscillators using Lindblad master equations and phase-space methods, with explicit examples of two and many coupled oscillators. We further discuss noise, synchronization measures, and the extreme quantum regime, including synchronization in spin systems. The emphasis throughout is on analytical derivations and a practical methodology for identifying synchronized states, determining their stability, and characterizing synchronization in quantum systems. The review is designed as a self-contained guide from which we hope that students can learn the essential concepts and techniques, while researchers can readily find the analytical tools and methodological insights needed to approach new synchronization problems.
The concept of quantum thermodynamic phase transfer (QTPT) proposes a new perspective on how thermodynamic transformations affect not only the entropy of a system but also its intrinsic quantum phase. In conventional thermodynamics, a process is often described solely by changes in macroscopic variables such as temperature, volume, and entropy. QTPT extends this view by introducing a phase variable φ_T that couples to thermodynamic forces during a transformation. This coupling is governed by a set of linear response relations that relate the change in φ_T to gradients of temperature and chemical potential, thereby unifying quantum coherence and classical thermodynamics within a single framework. The theory predicts measurable signatures in quantum heat engines and refrigerators, such as phase-dependent work output and entropy production that can be experimentally accessed through interferometric techniques. By offering a consistent description of how thermodynamic work can be harnessed to control quantum phases, QTPT opens pathways for designing high-efficiency quantum machines and for exploring fundamental limits of energy conversion in the quantum regime.