arXiv subjects

YiNuo Tian

Publications and source records attributed to YiNuo Tian.

4 recordsLinked to original sources

arXiv2025

A Heuristic Study of Temperature: Quantum Circuitry in Thermal Systems

The singularities prevalent in classical thermodynamics largely stem from the "postulate of equal a priori probabilities" neglecting the physical constraints imposed by computational complexity. This paper introduces Complexity Window Thermodynamics (CWT), a framework that characterizes the observer's "ignorance" via a finite complexity budget, thereby naturally smoothing out singular behaviors associated with phase transitions and negative temperatures within this window. We derive a generalized First Law of Thermodynamics driven by a complexity generation potential, which incorporates "information processing work," and demonstrate a universal action-time bound constraining the growth of complexity. CWT not only offers a unified perspective on critical phenomena in condensed matter and the black hole information problem but also suggests that the total generatable complexity of the universe is comparable in order of magnitude to its holographic entropy. Thus, it paves a new pathway for a resource-theoretic unification of thermodynamics, quantum computation, and gravity.

cond-mat.stat-mech↗

arXiv2025

Structure-Fair Quantum Circuit Complexity: An Auditable Information-Theoretic Lower Bound

Quantifying the complexity of quantum states that possess intrinsic structure, such as symmetry or encoding, in a fair manner constitutes a core challenge in the benchmarking of quantum technologies. This paper introduces the Reference-Contingent Complexity (RCC), an information-theoretic measure calibrated by the available quantum operations. The core idea is to leverage the quantum relative entropy to quantify the deviation of a quantum state from its "structured vacuum"-namely, the maximum entropy state within its constrained subspace-thereby only pricing the process of creating non-trivial information. Our central result is a key theorem that rigorously proves the RCC serves as a lower bound for the complexity of any universal quantum circuit. This lower bound is comprised of a linear dominant term, a universal logarithmic correction, and a precise physical correction term that accounts for non-uniformity in the spectral distribution. Crucially, we establish a set of operational protocols, grounded in tasks like quantum hypothesis testing, which make this theoretical lower bound experimentally "auditable." This work provides a "ruler" for quantum technology that is structure-fair and enables cross-platform comparison, thereby establishing a strictly verifiable constraint between the computational cost of the process and the structured information of the final state.

quant-ph↗

arXiv2025

The Cost of Nonlocality: A Dynamical Performance Equation of Energy-Entanglement-Complexity

This work aims to quantify the physical cost of generating non-local entanglement in systems governed by local interactions. By unifying the quantum speed limit and Lieb-Robinson bounds, we establish an "energy-entanglement performance equation." This framework connects theoretical computational complexity with experimental observables by introducing a measurable proxy for complexity, thereby revealing a performance trade-off among the "energy variance-entanglement product," the strength of local interactions, and dynamical efficiency. Our work not only defines a "performance frontier"-constrained by theoretical bounds and amenable to experimental benchmarking-but also provides a novel diagnostic tool for identifying the performance bottlenecks of a process.

quant-ph↗

arXiv2025

The Exploratory Study on the Relationship Between the Failure of Distance Metrics in High-Dimensional Space and Emergent Phenomena

This paper presents a unified framework, integrating information theory and statistical mechanics, to connect metric failure in high-dimensional data with emergence in complex systems. We propose the "Information Dilution Theorem," demonstrating that as dimensionality ($d$) increases, the mutual information efficiency between geometric metrics (e.g., Euclidean distance) and system states decays approximately as $O(1/d)$. This decay arises from the mismatch between linearly growing system entropy and sublinearly growing metric entropy, explaining the mechanism behind distance concentration. Building on this, we introduce information structural complexity ($C(S)$) based on the mutual information matrix spectrum and interaction encoding capacity ($C'$) derived from information bottleneck theory. The "Emergence Critical Theorem" states that when $C(S)$ exceeds $C'$, new global features inevitably emerge, satisfying a predefined mutual information threshold. This provides an operational criterion for self-organization and phase transitions. We discuss potential applications in physics, biology, and deep learning, suggesting potential directions like MI-based manifold learning (UMAP+) and offering a quantitative foundation for analyzing emergence across disciplines.

cs.IT↗