arXiv subjects

Hong Qian

Publications and source records attributed to Hong Qian.

At least 19 recordsLinked to original sources

arXiv2026

ProIQA: A Process-Based Framework for Fine-Grained Math Item Quality Assessment

Automatic Item Generation (AIG) is pivotal for personalized education, yet guaranteeing the pedagogical value of generated items remains a bottleneck. Existing Item Quality Assessment (IQA) methods typically rely on unscalable manual reviews or shallow stem-based metrics, failing to capture the reasoning process required for mathematical problem-solving. To bridge this gap, this paper proposes Process-based Item Quality Assessment (ProIQA), a process-aware framework for fine-grained quality assessment of math items. We first formulate IQA across three heterogeneous dimensions, including knowledge concepts, difficulty, and disciplinary competencies, under a unified process-aware perspective. Based on this formulation, we construct a process-enhanced IQA resource by augmenting original item data with structured reasoning trees derived from raw solutions. Technically, ProIQA leverages Large Language Modelsto construct hierarchical reasoning trees and employs Graph Neural Networks (GNN) to encode their topological dependencies and procedural semantics. The resulting solving representation is fused with stem semantics through a dual-view (``Stem + Solving'') architecture, enabling comprehensive assessment across learning objectives. Extensive experiments on K12 mathematical datasets show that ProIQA effectively captures process-oriented features, offering a scalable data-driven solution for evaluating AIG outputs in intelligent education systems.

cs.AI↗

arXiv2026

OptSkills: Learning Generalizable Optimization Skills from Problem Archetypes via Cluster-Based Distillation

Leveraging Large Language Models (LLMs) to automatically formulate and solve optimization problems from natural language has emerged as an efficient paradigm for automated optimization. However, existing methods still exhibit limited generalization: they are sensitive to superficial narrative variations, reuse experience mainly at the case level, and struggle to adapt to shifted or emerging problem types. We propose OptSkills, an archetype-centric skill learning and reasoning agent system for optimization modeling and solving. To improve robust generalization, our system clusters problems by their underlying archetypes rather than surface narratives. To improve in-distribution generalization, it explores diverse modeling paradigms and solver configurations within each cluster, then distills successful trajectories into reusable workflow-level skills. To improve out-of-distribution generalization, it refines existing skills or expands the skill library using newly obtained trajectories. Our system achieves a state-of-the-art micro-averaged accuracy of 68.27% on datasets encompassing diverse problem types and scenarios. In addition, on MIPLIB-NL, a highly challenging large-scale and high-dimensional benchmark, it achieves 26.91% accuracy, outperforming DeepSeek-V3.2-Thinking by 4.53%. After skill learning on Nano-CO, it reaches 72.79% on the OOD NLCO benchmark. Code and skills are available at https://github.com/fujiwaranoM0kou/OptSkills.

cs.AI↗

arXiv2026

MiniOpt: Reasoning to Model and Solve General Optimization Problems with Limited Resources

Achieving strong optimization generalization across diverse optimization problems while requiring limited training resources remains a challenging problem for optimization-oriented large language models (LLMs). Existing approaches typically rely on large-scale supervised datasets, costly reasoning annotations, and expensive intermediate step verification, resulting in substantial training overhead. To address these challenges, we propose MiniOpt, a reinforcement learning framework that learns to solve optimization problems through an "reasoning-to-model-and-solve" paradigm. MiniOpt decomposes optimization reasoning into structured optimization modeling and executable solver generation. Building upon this paradigm, we introduce OptReward, a reward function with hierarchical score structure that jointly evaluates formulation and solution, enabling effective policy learning without expert demonstrations. We further develop an optimization-oriented policy optimization strategy that improves exploration efficiency and stabilizes reinforcement learning for compact models. Extensive experiments show that MiniOpt-3B exhibits strong optimization generalization across various optimization types, problem scenarios, and task domains. For models with fewer than 10B parameters, MiniOpt series achieves the highest average solving accuracy (SA). For models with more than 10B parameters, MiniOpt still shows competitive performance. These results suggest that optimization-oriented reward design and reinforcement learning provide an effective pathway for developing compact optimization-specialized language models with strong optimization generalization capabilities. The code is available at https://github.com/Hsiang-1/MiniOpt.

cs.LG↗

arXiv2026

DEFINED: A Data-Efficient Computational Framework for Fine-Grained Creativity Assessment in Debate Scenarios

Human creativity has emerged as a critical competency in the era of large language models. Assessing creativity in complex, open-ended environments is a grand challenge in data mining, currently hindered by a reliance on standardized simple tasks and the scarcity of fine-grained expert data. As an ecologically valid assessment context, debate reflects multiple dimensions of creativity, encompassing both divergent thinking and convergent thinking. Moreover, debate is a data-rich domain, with a large volume of publicly accessible materials. Current mainstream automated scoring methods are poorly suited to complex settings such as debate, and therefore still rely on costly human evaluation. To this end, this paper proposes DEFINED, a data-efficient computational framework for fine-grained creativity assessment in debate scenarios. DEFINED operationalizes debate creativity through a hierarchical eight-dimensional metric system, implemented via a pre-trained autoregressive language model with a hierarchical scoring head that supports both fine-grained and coarse-grained evaluation. Statements and their associated expert scores were obtained from authentic debate competitions, and a constrained data augmentation strategy was employed to address the elite bias inherent in the original data. DEFINED adopts a mixed-granularity training strategy enabling robust learning from limited fine-grained supervision annotated by trained graduate experts. To rigorously validate ecological validity beyond synthetic benchmarks, we incorporate an empirical study with debate-naive participants, utilizing these authentic data to serve as a qualitative case study for mid-to-low proficiency populations. Across our evaluation protocol, our scoring model achieves accurate and stable scoring, outperforming prompt-based large language model evaluators and existing debate scoring methods.

cs.LG↗

arXiv2026

Diversity-Driven Offline Multi-Objective Optimization via Nested Pareto Set Learning

Multi-objective optimization (MOO) has emerged as a powerful approach to solving complex optimization problems involving multiple objectives. In many practical scenarios, function evaluations are unavailable or prohibitively expensive, necessitating optimization solely based on a fixed offline dataset. In this setting, known as offline MOO, the goal is to find out the Pareto set without access to the true objective functions. This setting suffers from the out-of-distribution (OOD) issue, where the surrogate model is not accurate for unseen designs. Due to the OOD issue, surrogate errors may cause the optimizer to select solutions that do not lie on the true Pareto front and are biased toward its extremes. To address this, this paper proposes Diversity-driven Offline Multi-Objective Optimization (DOMOO), which aims to find out a diverse and high-quality set of solutions. First, DOMOO incorporates an accumulative risk control module that estimates the potential risk of candidate solutions and alleviates the OOD issue between the training data and the generated solutions. In addition, a nested Pareto set learning (PSL) strategy is proposed to jointly learn preference and PSL parameters, then optimize them, enabling adaptation to diverse Pareto front geometries. To further enhance solution quality, we design a diversity-driven selection strategy that extracts a representative and well-distributed set of final solutions. To achieve this diversity-driven selection strategy, we propose $\text{IGD}_\text{offline}$, a tailored indicator for the offline setting that considers both diversity and convergence, and avoids the bias of hypervolume indicator. Extensive experiments on synthetic and real-world benchmarks show that DOMOO achieves the best average rank across tasks in both convergence and diversity among the compared methods.

cs.LG↗

arXiv2026

IntElicit: Eliciting and Assessing Contextualized Creativity via Dialogue Policy Optimization

Contextualized assessment offers high ecological validity for evaluating creativity but introduces a critical challenge: observed performance may be confounded with cognitive proficiency (domain knowledge) and agency (willingness to engage). Meanwhile, in the age of generative AI, creative problem solving increasingly occurs in tool-mediated and human--AI interactive environments, making fully static assessment less aligned with contemporary creative practice. To address these issues, this paper proposes IntElicit, a framework for eliciting and assessing contextualized creativity via dialogue policy optimization. IntElicit functions as a constrained adaptive AI Interviewer: it provides non-directive knowledge and agency scaffolds in multi-turn interaction to reduce non-creative confounders, while preserving participants' responsibility for generating the creative content being evaluated. Specifically, to tackle sparse rewards and potential reward hacking (e.g., answer dictation) in open-ended educational dialogue, IntElicit introduces a decomposed process reward mechanism. This mechanism aligns the policy with pedagogical elicitation, rewarding prompts that draw out participant reasoning rather than producing optimal answers on their behalf. Extensive experiments, including participant simulation and a human subject study (N=64), show that IntElicit improves elicited creative outcomes over expert-designed baselines. Together, the results suggest that interactive elicitation can reveal creative potential that static FPSP-style assessment may miss, providing a formative and diagnostic lens for contextualized creativity assessment in AI-mediated learning contexts.

cs.AI↗

arXiv2026

CollabBench: Benchmarking and Unleashing Collaborative Ability of LLMs with Diverse Players via Proactive Engagement

While LLM-based agents excel at individual tasks, effective collaboration with realistic human partners remains challenging. Most of the existing conversation-level collaborative studies lack grounded interaction and behavioral execution, motivating the need for cooperative game environments that enable contextualized and immersive collaboration. To this end, this paper proposes CollabBench, a benchmark for evaluating and training collaborative agents in cooperative games. CollabBench features a Diverse Player Profile Simulation pipeline to model varied players behaviors, and a Collaborative Agentic Training paradigm that unifies reasoning, communication, and action via agentic rollouts, optimized with a hybrid reward balancing task efficiency and affective adaptation. We further extend classic environments to CWAH-MultiPlayer and Cook-MultiPlayer for systematic evaluation under diverse personalities. Experiments with efficiency and affective metrics show that our trained models outperform base models, achieving 19.5% higher efficiency and 24.4% improved affective performance. Further analysis reveals key collaborative limitations of existing models and offers insights for future collaborative training.

cs.CL↗

arXiv2026

AgentSchool: An LLM-Powered Multi-Agent Simulation for Education

Despite the rapid deployment of LLMs into classrooms, validating educational AI remains uniquely intractable: interventions act on developing learners whose cognitive and social trajectories are irreversibly shaped, while real-world trials are slow, ethically constrained, and institutionally locked. LLM-based educational simulators have emerged as a potential remedy, but many still collapse learning into persona-conditioned role-play and, when optimized only to reproduce existing classrooms, can structurally penalize the institutional novelty that pedagogical reform requires. In this work, we introduce AgentSchool, an LLM-driven multi-agent simulator that models learning as state transition rather than prompted behavior. AgentSchool couples cognitively growable student agents -- equipped with weighted subject knowledge graphs, thinking-workflow pools, and explicit misconceptions -- with adaptive teacher agents that plan, scaffold, and reflect along the Zone of Proximal Development, embedded in a configurable scenery generator that situates instruction within both formal and informal learning fields, and a multi-scale simulator that decouples interaction scale, temporal granularity, and simulation duration. Experiments show that structured student agents produce more differentiated mastery and misconception traces than a baseline simulator, while teacher-agent comparisons show backbone-dependent patterns consistent with ZPD-informed adaptation. Further, AgentSchool generates plausible traces of peripheral participation, clique formation, aggressor-induced cohesion, and opinion-leader emergence consistent with classroom social theories. Beyond its role as an educational research instrument, AgentSchool frames education as a socially meaningful testbed for long-horizon memory, multi-agent coordination, and future institutional reasoning under organizational pressure.

cs.AI↗

arXiv2026

Automated Random Embedding for Practical Bayesian Optimization with Unknown Effective Dimension

Bayesian optimization is widely employed for optimizing complex black-box functions but struggles with the curse of dimensionality. Random embedding, as a dimension reduction strategy, simplifies tasks that possess the effective dimension by optimizing within a low-dimensional subspace. However, determining the effective dimension of a task in advance remains a significant challenge, which influences the selection of the subspace dimensionality and the optimization performance. Traditional methods use fixed subspace dimensions provided by experts or rely on trial and error to estimate subspace dimensions with resources consumed. To this end, this paper proposes an automated random embedding for high-dimensional Bayesian optimization with unknown effective dimension, called Dynamic Shared Embedding Bayesian Optimization (DSEBO). DSEBO starts with a low dimension and switches to a higher subspace if the solutions in the current subspace show preliminary convergence. DSEBO dynamically determines the dimension of the next subspace based on the quality of the solutions in different subspaces and shares the queried solutions with the new subspace for a better initialization. Theoretically, we derive a regret bound for DSEBO and demonstrate that DSEBO can better balance approximation and optimization errors. Extensive experiments on functions with dimensionality of varying magnitudes and real-world tasks with unknown effective dimensions reveal that, compared with state-of-the-art methods, alternating optimization across different subspaces results in significant improvements in high-dimensional optimization, both in terms of optimization regret and time.

cs.LG↗

arXiv2026

The Geometry of Statistical Data and Information: A Large Deviation Perspective

The manifold of empirical mean values of statistical data ad infinitum has a geometric shape that depends on the probability measure that governs the generating model. Large deviation theory produces entropy functions that depend on both the probability measure and the statistical data; we use entropy to study the geometry of the data space rather than that of the space of probability distributions. It is well known, since Rao's work, that the Fisher-Rao metric makes the probability simplex into a sphere. From our perspective, that result translates to the space of empirical singleton counting frequencies under an i.i.d. assumption. Following our ideas and going beyond i.i.d., the choice of measure curves the space. When we study the pairwise statistics, the spherical geometry breaks down entirely. We show that the information projection, defined in information geometry as divergence minimization, coincides with the information projection in Kolmogorov's probability theory. This identification holds under both i.i.d. and Markovian assumptions and connects information geometry to the foundations of probability theory.

cs.IT↗

arXiv2026

AlphaContext: An Evolutionary Tree-based Psychometric Context Generator for Creativity Assessment

Creativity has become a core competence in the era of LLMs and human-AI collaboration, underpinning innovation in real-world problem solving. Crucially, the systematic improvement of creativity necessitates scientifically valid assessment instruments. Psychometric research recognizes context-based assessment as an effective way to measure creative thinking. However, high-quality expert-designed contexts remain scarce. Existing LLM-based generators often struggle with insufficient assessment cues, weak narrative coherence, limited stylistic diversity, and poor support for creative thinking. To address these challenges, we propose AlphaContext, an evolutionary tree-based psychometric context generator for creativity assessment. First, the HyperTree Outline Planner formalizes expert-designed outlining as a rule-guided hypertree and performs top-down hierarchical planning. The MCTS-based Context Generator fills the outline via MCTS to balance global structure and local quality. Then, the Evolutionary Context Optimizer evolves contexts with MAP-Elites by repeatedly updating niche elites to jointly improve diversity and quality. Finally, the Assessment-Guided Evolution Refiner simulates virtual participants with diverse styles and recycles weak contexts for further evolution. Experiments show that AlphaContext yields an average improvement of 8% over competitive methods across 6 quality metrics.

cs.CL↗

arXiv2026

Embedding Enhancement via Fine-Tuned Language Models for Learner-Item Cognitive Modeling

Learner-item cognitive modeling plays a central role in the web-based online intelligent education system by enabling cognitive diagnosis (CD) across diverse online educational scenarios. Although ID embedding remains the mainstream approach in cognitive modeling due to its effectiveness and flexibility, recent advances in language models (LMs) have introduced new possibilities for incorporating rich semantic representations to enhance CD performance. This highlights the need for a comprehensive analysis of how LMs enhance embeddings through semantic integration across mainstream CD tasks. This paper identifies two key challenges in fully leveraging LMs in existing work: Misalignment between the training objectives of LMs and CD models creates a distribution gap in feature spaces; A unified framework is essential for integrating textual embeddings across varied CD tasks while preserving the strengths of existing cognitive modeling paradigms to ensure the robustness of embedding enhancement. To address these challenges, this paper introduces EduEmbed, a unified embedding enhancement framework that leverages fine-tuned LMs to enrich learner-item cognitive modeling across diverse CD tasks. EduEmbed operates in two stages. In the first stage, we fine-tune LMs based on role-specific representations and an interaction diagnoser to bridge the semantic gap of CD models. In the second stage, we employ a textual adapter to extract task-relevant semantics and integrate them with existing modeling paradigms to improve generalization. We evaluate the proposed framework on four CD tasks and computerized adaptive testing (CAT) task, achieving robust performance. Further analysis reveals the impact of semantic information across diverse tasks, offering key insights for future research on the application of LMs in CD for online intelligent education systems.

cs.CL↗

arXiv2026

A Comprehensive Exploration of Personalized Learning in Smart Education: From Student Modeling to Personalized Recommendations

With the development of artificial intelligence, personalized learning has attracted much attention as an integral part of intelligent education. In recent years, countries and regions such as China, the United States, and the European Union have increasingly recognized the importance of personalized learning, emphasizing its potential to integrate large-scale education with individualized instruction effectively. This survey provides a comprehensive analysis of personalized learning by reviewing relevant studies published in major conferences and journals between January 2017 and April 2025. We examine its definition, objectives, and underlying educational theories, highlighting its pedagogical significance. Furthermore, we explore personalized learning from two key dimensions: student modeling and personalized recommendations. Student modeling is analyzed from both cognitive and non-cognitive perspectives, while recommendation approaches are categorized based on their specific objectives. Additionally, we investigate the interplay between these components and their role in enhancing personalized learning. Beyond theoretical and algorithmic insights, this survey reviews real-world applications, demonstrating personalized learning's effectiveness in educational practice. Finally, we discuss key challenges and future directions, offering a multidimensional perspective that bridges theory and practice.

cs.CY↗

arXiv2025

Kinetic and Thermodynamic Descriptions of Open Systems of Complex Chemical Reactions with Multiple Scales

The general theory of a complex system of nonlinear chemical reactions is a primary language of chemistry that includes chemical engineering and cellular biochemistry. Its significance as an analytical framework, however, has not been fully appreciated outside the community of physical chemists. In this review, we discuss the latest advances in the kinetics and Gibbsian thermodynamics of chemical reactions in a spatially homogeneous aqueous solution with a multiscale perspective on complex systems. From the microscopic level of single reaction events which are purely stochastic in continuous time, one at a time among a set of molecules, to the macroscopic chemical reaction systems in bulk in terms of deterministic rate equations, the mathematical descriptions of kinetic models for chemical reactions at different levels are presented in detail, with rigorous mathematical justifications presented. In parallel with the kinetics of chemical reactions, the irreversible thermodynamics of open systems and the stochastic thermodynamics along reactions trajectories are reviewed thoroughly. As a novel feature, the mathematical theory of large deviations is shown to play a pivotal role in the thermodynamics of chemical reactions in equilibrium and in irreversible processes. This review is expected to stimulate interests in and help defining multiscale phenomena and nonequilibrium thermodynamics in many research fields on population dynamics of interacting species using chemical reactions as an analytic paradigm.

physics.chem-ph↗

arXiv2025

Neo-Gibbsian Statistical Energetics with Applications to Nonequilibrium Cells

Generalization through novel interpretations of the inner logic of the century-old Gibbs' statistical thermodynamics is presented: i) Identifying $k_B\to 0$ as classical energetics, one directly derives a pair of thermodynamic variational formulae \[ F(T) = \min_{E\ge E_{min}}\Big\{E-TS(E) \Big\} \,\text{ and }\ S(E) = \min_{T>0}\left\{\frac{E}{T}-\frac{F(T)}{T} \right\}, \] that dictate all the more familiar $1/T=d S(E)/d E$, $E=d\{F(T)/T\}/d(1/T)$, and $S(E)=-d F(T)/d T$ in equilibrium, which is maintained by a duality symmetry with one-to-one relation between $T^{\text{eq}}(E)=\arg\min_T\{E/T-F(T)/T\}$ and $E^{\text{eq}}(T)=\arg\min_E\{E-TS(E)\}$. ii) In contradistinction, taking derivative of the statistical free energy w.r.t. $T$, a mesoscopic energetics with fluctuations emerges: This yields two information entropy functions which historically appeared 50 years postdate Gibbs' theory. iii) Combining the above pair of inequalities yields an irreversible thermodynamic potential $ψ(T,E) \equiv \{E-F(T)\}/T-S(E)\ge 0$ for nonequilibrium states. The second law of thermodynamics as a universal principle reflects $ψ\ge 0$ due to a disagreement between $E$ and $T$ as a dual pair. Our theory provides a new energetics of living cells which are nonequilibrium, complex entities under constant $T$, pressure $p$ and chemical potential $μ$. $ψ$ provides a ``distance'' between statistical data from a large ensemble of cells and a set of intrinsic energetic parameters that encode the information within.

cond-mat.stat-mech↗

arXiv2025

Surrogate-Assisted Evolutionary Reinforcement Learning Based on Autoencoder and Hyperbolic Neural Network

Evolutionary Reinforcement Learning (ERL), training the Reinforcement Learning (RL) policies with Evolutionary Algorithms (EAs), have demonstrated enhanced exploration capabilities and greater robustness than using traditional policy gradient. However, ERL suffers from the high computational costs and low search efficiency, as EAs require evaluating numerous candidate policies with expensive simulations, many of which are ineffective and do not contribute meaningfully to the training. One intuitive way to reduce the ineffective evaluations is to adopt the surrogates. Unfortunately, existing ERL policies are often modeled as deep neural networks (DNNs) and thus naturally represented as high-dimensional vectors containing millions of weights, which makes the building of effective surrogates for ERL policies extremely challenging. This paper proposes a novel surrogate-assisted ERL that integrates Autoencoders (AE) and Hyperbolic Neural Networks (HNN). Specifically, AE compresses high-dimensional policies into low-dimensional representations while extracting key features as the inputs for the surrogate. HNN, functioning as a classification-based surrogate model, can learn complex nonlinear relationships from sampled data and enable more accurate pre-selection of the sampled policies without real evaluations. The experiments on 10 Atari and 4 Mujoco games have verified that the proposed method outperforms previous approaches significantly. The search trajectories guided by AE and HNN are also visually demonstrated to be more effective, in terms of both exploration and convergence. This paper not only presents the first learnable policy embedding and surrogate-modeling modules for high-dimensional ERL policies, but also empirically reveals when and why they can be successful.

cs.LG↗

arXiv2025

Preference Diffusion for Recommendation

Recommender systems predict personalized item rankings based on user preference distributions derived from historical behavior data. Recently, diffusion models (DMs) have gained attention in recommendation for their ability to model complex distributions, yet current DM-based recommenders often rely on traditional objectives like mean squared error (MSE) or recommendation objectives, which are not optimized for personalized ranking tasks or fail to fully leverage DM's generative potential. To address this, we propose PreferDiff, a tailored optimization objective for DM-based recommenders. PreferDiff transforms BPR into a log-likelihood ranking objective and integrates multiple negative samples to better capture user preferences. Specifically, we employ variational inference to handle the intractability through minimizing the variational upper bound and replaces MSE with cosine error to improve alignment with recommendation tasks. Finally, we balance learning generation and preference to enhance the training stability of DMs. PreferDiff offers three key benefits: it is the first personalized ranking loss designed specifically for DM-based recommenders and it improves ranking and faster convergence by addressing hard negatives. We also prove that it is theoretically connected to Direct Preference Optimization which indicates that it has the potential to align user preferences in DM-based recommenders via generative modeling. Extensive experiments across three benchmarks validate its superior recommendation performance and commendable general sequential recommendation capabilities. Our codes are available at https://github.com/lswhim/PreferDiff.

cs.IR↗

arXiv2025

Mesoscopic and Macroscopic Entropy Balance Equations in a Stochastic Dynamics and Its Deterministic Limit

Entropy, its production, and its change in a dynamical system can be understood from either a fully stochastic dynamic description or from a deterministic dynamics exhibiting chaotic behavior. By taking the former approach based on the general diffusion process with diffusion $\tfrac{1}α{\bf D}(\bf x)$ and drift $\bf b(\bf x)$, where $α$ represents the ``size parameter'' of a system, we show that there are two distinctly different entropy balance equations. One reads ${\rm d} S^{(α)}/{\rm d} t = e^{(α)}_p + Q^{(α)}_{ex}$ for all $α$. However, the leading $α$-order, ``extensive'', terms of the entropy production rate $e^{(α)}_p$ and heat exchange rate $Q^{(α)}_{ex}$ are exactly cancelled. Therefore, in the asymptotic limit of $α\to\infty$, there is a second, local ${\rm d} S/{\rm d} t = \nabla\cdot{\bf b}({\bf x}(t))+\left({\bf D}:{\bf Σ}^{-1}\right)({\bf x}(t))$ on the order of $O(1)$, where $\tfrac{1}α{\bf D}(\bf x(t))$ represents the randomness generated in the dynamics usually represented by metric entropy, and $\tfrac{1}α{\bf Σ}({\bf x}(t))$ is the covariance matrix of the local Gaussian description at ${\bf x}(t)$, which is a solution to the ordinary differential equation $\dot{\bf x}={\bf b}(\bf x)$ at time $t$. This latter equation is akin to the notions of volume-preserving conservative dynamics and entropy production in the deterministic dynamic approach to nonequilibrium thermodynamics {\it à la} D. Ruelle. As a continuation of [17], mathematical details with sufficient care are given in four Appendices.

math-ph↗