Advanced Thermodynamics and Statistical Mechanics

Latest papers

• ELEMENT: Episodic and Lifelong Exploration via Maximum Entropy

  Hongming Li, Zhao Yang, Xiaoxuan Liang, Shujian Yu, Jose C. Principe · 23 September 2026

  Reinforcement learning agents depend on reward signals whose density is rarely under the designer's control, and when such signals are absent, an agent must generate its own drive to explore. State entropy maximization offers a principled objective for this, but existing methods break down at scale …

• Blind Thermodynamic Ontology Discovery from Anonymous Experiments

  Linzhe Zhang, Changming Xu · 22 September 2026

  Before a machine learning model can learn a thermodynamic equation of state, it must discover what its measurements represent: which channels scale with system size, which are intensive conjugates, how sectors pair through contact, and which potential governs stability. When sensors expose only an u…

• Quantum Maximum Entropy Inference and Hamiltonian Learning

  Minbo Gao, Zhengfeng Ji, Fuchao Wei · 26 August 2026

  Maximum entropy inference and learning of graphical models are pivotal tasks in learning theory and optimization. This work extends algorithms for these problems, including generalized iterative scaling (GIS) and gradient descent (GD), to the quantum realm. While the generalization, known as quantum…

• Leveraging Machine Learning to Gain Insights on Quantum Thermodynamic Entropy

  Srinivasa Rao. P · 6 August 2026

  We present a thermodynamic analysis of a quantum engine that uses a single quantum particle as its working fluid, inspired by Szilard's classical single-particle engine. Our design is modeled after the classically-chaotic Szilard Map and involves a thermodynamic cycle of measurement, thermal-energy …

• Accelerated sampling using SamAdams variable timesteps and position-adaptive Langevin dynamics

  Benedict Leimkuhler, Peter A. Whalley · 26 June 2026

  We introduce an accelerated Langevin-based sampling method that is based on two complementary devices: \emph{SamAdams} adaptive timestepping, which automatically shrinks the effective integration step in stiff regions of phase space using a relaxed stiffness monitor, and \emph{position-adaptive Lang…

• Stochastic Thermodynamics and SDE-based Generative Models

  Yaowen Zhang · 18 June 2026

  SDE-based generative models, including diffusion models and the Schr\"odinger bridge, have found broad applications in signal processing tasks such as speech enhancement, image restoration, and time-series generation. This note presents a modeling framework for such models within the context of stoc…

• Structure learning of Hamiltonians from real-time evolution

  Ainesh Bakshi, Allen Liu, Ankur Moitra, Ewin Tang · 11 May 2026

  We study the problem of Hamiltonian structure learning from real-time evolution: given the ability to apply $e^{-\mathrm{i} Ht}$ for an unknown local Hamiltonian $H = \sum_{a = 1}^m \lambda_a E_a$ on $n$ qubits, the goal is to recover $H$. This problem is already well-understood under the assumption…

• Mean-Field Path-Integral Diffusion: From Samples to Interacting Agents

  Michael Chertkov · 4 May 2026

  Independent sample generation is the prevailing paradigm in modern diffusion-based generative models of AI. We ask a different question: can samples \emph{coordinate} through shared population statistics to transport probability mass more efficiently? We introduce Mean-Field Path-Integral Diffusion …

• Thermodynamic Diffusion Inference with Minimal Digital Conditioning

  Aditi De · 17 April 2026

  Diffusion-model inference and overdamped Langevin dynamics are formally identical. A physical substrate that encodes the score function therefore equilibrates to the correct output by thermodynamics alone, requiring no digital arithmetic during inference and potentially achieving a $10{,}000\times$ …

• Automated co-design of high-performance thermodynamic cycles via graph-based hierarchical reinforcement learning

  Wenqing Li, Xu Feng, Peixue Jiang, Yinhai Zhu · 16 April 2026

  Thermodynamic cycles are pivotal in determining the efficacy of energy conversion systems. Traditional design methodologies, which rely on expert knowledge or exhaustive enumeration, are inefficient and lack scalability, thereby constraining the discovery of high-performance cycles. In this study, w…

• Contextuality from Single-State Ontological Models: An Information-Theoretic Obstruction

  Song-Ju Kim · 16 April 2026

  Contextuality is a central feature of quantum theory, traditionally understood as the impossibility of reproducing quantum measurement statistics using noncontextual ontological models. We study classical ontological descriptions in which a fixed subsystem-level ontic state space is reused across mu…

• Learning thermodynamic master equations for open quantum systems

  Peter Sentz, Stanley Nicholson, Yujin Cho, Sohail Reddy, Brendan Keith, Stefanie G\"unther · 7 April 2026

  The characterization of Hamiltonians and other components of open quantum dynamical systems plays a crucial role in quantum computing and other applications. Scientific machine learning techniques have been applied to this problem in a variety of ways, including by modeling with deep neural networks…

• Reinforcement learning for quantum processes with memory

  Josep Lumbreras, Ruo Cheng Huang, Yanglin Hu, Marco Fanizza, Mile Gu · 27 March 2026

  In reinforcement learning, an agent interacts sequentially with an environment to maximize a reward, receiving only partial, probabilistic feedback. This creates a fundamental exploration-exploitation trade-off: the agent must explore to learn the hidden dynamics while exploiting this knowledge to m…

• Geometric Learning Dynamics

  Vitaly Vanchurin · 17 March 2026

  We present a unified geometric framework for modeling learning dynamics in physical, biological, and machine learning systems. The theory reveals three fundamental regimes, each emerging from the power-law relationship $g \propto \kappa^\alpha$ between the metric tensor $g$ in the space of trainable…

• Thermodynamics of Reinforcement Learning Curricula

  Jacob Adamczyk, Juan Sebastian Rojas, Rahul V. Kulkarni · 16 March 2026

  Connections between statistical mechanics and machine learning have repeatedly proven fruitful, providing insight into optimization, generalization, and representation learning. In this work, we follow this tradition by leveraging results from non-equilibrium thermodynamics to formalize curriculum l…

• On Emergences of Non-Classical Statistical Characteristics in Classical Neural Networks

  Hanyu Zhao, Yang Wu, Yuexian Hou · 6 March 2026

  Inspired by measurement incompatibility and Bell-family inequalities in quantum mechanics, we propose the Non-Classical Network (NCnet), a simple classical neural architecture that stably exhibits non-classical statistical behaviors under typical and interpretable experimental setups. We find non-cl…

• Convergence, Sticking and Escape: Stochastic Dynamics Near Critical Points in SGD

  Dmitry Dudukalov, Artem Logachov, Vladimir Lotov, Timofei Prasolov, Evgeny Prokopenko, Anton Tarasenko · 5 March 2026

  We study the convergence properties and escape dynamics of Stochastic Gradient Descent (SGD) in one-dimensional landscapes, separately considering infinite- and finite-variance noise. Our main focus is to identify the time scales on which SGD reliably moves from an initial point to the local minimum…

• Contextuality from Single-State Ontological Models: An Information-Theoretic No-Go Theorem

  Song-Ju Kim · 24 February 2026

  Contextuality is a central feature of quantum theory, traditionally understood as the impossibility of reproducing quantum measurement statistics using noncontextual ontological models. We consider classical ontological models constrained to reuse a single ontic state space across multiple intervent…

• Contextuality from Single-State Representations: An Information-Theoretic Principle for Adaptive Intelligence

  Song-Ju Kim · 20 February 2026

  Adaptive systems often operate across multiple contexts while reusing a fixed internal state space due to constraints on memory, representation, or physical resources. Such single-state reuse is ubiquitous in natural and artificial intelligence, yet its fundamental representational consequences rema…

• Generating Physical Dynamics under Priors

  Zihan Zhou, Xiaoxue Wang, Tianshu Yu · 16 February 2026

  Generating physically feasible dynamics in a data-driven context is challenging, especially when adhering to physical priors expressed in specific equations or formulas. Existing methodologies often overlook the integration of physical priors, resulting in violation of basic physical laws and subopt…

• Thermodynamic Limits of Physical Intelligence

  Koichi Takahashi, Yusuke Hayashi · 6 February 2026

  Modern AI systems achieve remarkable capabilities at the cost of substantial energy consumption. To connect intelligence to physical efficiency, we propose two complementary bits-per-joule metrics under explicit accounting conventions: (1) Thermodynamic Epiplexity per Joule -- bits of structural inf…

• Controllable Information Production

  Tristan Shah, Stas Tiomkin · 2 February 2026

  Intrinsic Motivation (IM) is a paradigm for generating intelligent behavior without external utilities. The existing information-theoretic methods for IM are predominantly based on information transmission, which explicitly depends on the designer's choice of which random variables engage in transmi…

• A Thermodynamic Theory of Learning I: Irreversible Ensemble Transport and Epistemic Costs

  Daisuke Okanohara · 29 January 2026

  Learning systems acquire structured internal representations from data, yet classical information-theoretic results state that deterministic transformations do not increase information. This raises a fundamental question: how can learning produce abstraction and insight without violating information…

• Exploring the Frontiers of Softmax: Provable Optimization, Applications in Diffusion Model, and Beyond

  Yang Cao, Yingyu Liang, Zhenmei Shi, Zhao Song · 27 January 2026

  The softmax activation function plays a crucial role in the success of large language models (LLMs), particularly in the self-attention mechanism of the widely adopted Transformer architecture. However, the underlying learning dynamics that contribute to the effectiveness of softmax remain largely u…

• Reinforcement Learning for Charging Optimization of Inhomogeneous Dicke Quantum Batteries

  Xiaobin Song, Siyuan Bai, Da-Wei Wang, Hanxiao Tao, Xizhe Wang, Rebing Wu, Benben Jiang · 26 January 2026

  Charging optimization is a key challenge to the implementation of quantum batteries, particularly under inhomogeneity and partial observability. This paper employs reinforcement learning to optimize piecewise-constant charging policies for an inhomogeneous Dicke battery. We systematically compare po…