Evaluating faithfulness of Large Language Models (LLMs) to a given task is a complex challenge. We propose two new unsupervised metrics for faithfulness evaluation using insights from information theory and thermodynamics. Our approach treats an LLM as a bipartite information engine where hidden layers act as a Maxwell demon controlling transformations of context $C $ into answer $A$ via prompt $Q$. We model Question-Context-Answer (QCA) triplets as probability distributions over shared topics. Topic transformations from $C$ to $Q$ and $A$ are modeled as transition matrices ${\bf Q}$ and ${\bf A}$ encoding the query goal and actual result, respectively. Our semantic faithfulness (SF) metric quantifies faithfulness for any given QCA triplet by the Kullback-Leibler (KL) divergence between these matrices. Both matrices are inferred simultaneously via convex optimization of this KL divergence, and the final SF metric is obtained by mapping the minimal divergence onto the unit interval [0,1], where higher scores indicate greater faithfulness. Furthermore, we propose a thermodynamics-based semantic entropy production (SEP) metric in answer generation, and show that high faithfulness generally implies low entropy production. The SF and SEP metrics can be used jointly or separately for LLM evaluation and hallucination control. We demonstrate our framework on LLM summarization of corporate SEC 10-K filings.

Large language model safety is usually assessed with static benchmarks, but key failures are dynamic: value drift under distribution shift, jailbreak attacks, and slow degradation of alignment in deployment. Building on a recent Second Law of Intelligence that treats ethical entropy as a state variable which tends to increase unless countered by alignment work, we make this framework operational for large language models. We define a five-way behavioral taxonomy, train a classifier to estimate ethical entropy S(t) from model transcripts, and measure entropy dynamics for base and instruction-tuned variants of four frontier models across stress tests. Base models show sustained entropy growth, while tuned variants suppress drift and reduce ethical entropy by roughly eighty percent. From these trajectories we estimate an effective alignment work rate gamma_eff and embed S(t) and gamma_eff in a monitoring pipeline that raises alerts when entropy drift exceeds a stability threshold, enabling run-time oversight of value drift.

We propose that unconstrained artificial intelligence obeys a Second Law analogous to thermodynamics, where ethical entropy, defined as a measure of divergence from intended goals, increases spontaneously without continuous alignment work. For gradient-based optimizers, we define this entropy over a finite set of goals {g_i} as S = -Σ p(g_i; theta) ln p(g_i; theta), and we prove that its time derivative dS/dt >= 0, driven by exploration noise and specification gaming. We derive the critical stability boundary for alignment work as gamma_crit = (lambda_max / 2) ln N, where lambda_max is the dominant eigenvalue of the Fisher Information Matrix and N is the number of model parameters. Simulations validate this theory. A 7-billion-parameter model (N = 7 x 10^9) with lambda_max = 1.2 drifts from an initial entropy of 0.32 to 1.69 +/- 1.08 nats, while a system regularized with alignment work gamma = 20.4 (1.5 gamma_crit) maintains stability at 0.00 +/- 0.00 nats (p = 4.19 x 10^-17, n = 20 trials). This framework recasts AI alignment as a problem of continuous thermodynamic control, providing a quantitative foundation for maintaining the stability and safety of advanced autonomous systems.

We propose a method for inferring entropy production (EP) in high-dimensional stochastic systems, including many-body systems and non-Markovian systems with long memory. Standard techniques for estimating EP become intractable in such systems due to computational and statistical limitations. We infer trajectory-level EP and lower bounds on average EP by exploiting a nonequilibrium analogue of the Maximum Entropy principle, along with convex duality. Our approach uses only samples of trajectory observables, such as spatiotemporal correlations. It does not require reconstruction of high-dimensional probability distributions or rate matrices, nor impose any special assumptions such as discrete states or multipartite dynamics. In addition, it may be used to compute a hierarchical decomposition of EP, reflecting contributions from different interaction orders, and it has an intuitive physical interpretation as a "thermodynamic uncertainty relation." We demonstrate its numerical performance on a disordered nonequilibrium spin model with 1000 spins and a large neural spike-train dataset.

Generative diffusion models have emerged as a powerful class of models in machine learning, yet a unified theoretical understanding of their operation is still developing. This perspective paper provides an integrated perspective on generative diffusion by connecting their dynamic, information-theoretic, and thermodynamic properties under a unified mathematical framework. We demonstrate that the rate of conditional entropy production during generation (i.e. the generative bandwidth) is directly governed by the expected divergence of the score function's vector field. This divergence, in turn, is linked to the branching of trajectories and generative bifurcations, which we characterize as symmetry-breaking phase transitions in the energy landscape. This synthesis offers a powerful insight: the process of generation is fundamentally driven by the controlled, noise-induced breaking of (approximate) symmetries, where peaks in information transfer correspond to critical transitions between possible outcomes. The score function acts as a dynamic non-linear filter that regulates the bandwidth of the noise by suppressing fluctuations that are incompatible with the data.

Markedly increased computational power and data acquisition have led to growing interest in data-driven inverse dynamics problems. These seek to answer a fundamental question: What can we learn from time series measurements of a complex dynamical system? For small systems interacting with external environments, the effective dynamics are inherently stochastic, making it crucial to properly manage noise in data. Here, we explore this for systems obeying Langevin dynamics and, using currents, we construct a learning framework for stochastic modeling. Currents have recently gained increased attention for their role in bounding entropy production (EP) from thermodynamic uncertainty relations (TURs). We introduce a fundamental relationship between the cumulant currents there and standard machine-learning loss functions. Using this, we derive loss functions for several key thermodynamic functions directly from the system dynamics without the (common) intermediate step of deriving a TUR. These loss functions reproduce results derived both from TURs and other methods. More significantly, they open a path to discover new loss functions for previously inaccessible quantities. Notably, this includes access to per-trajectory entropy production, even if the observed system is driven far from its steady-state. We also consider higher order estimation. Our method is straightforward and unifies dynamic inference with recent approaches to entropy production estimation. Taken altogether, this reveals a deep connection between diffusion models in machine learning and entropy production estimation in stochastic thermodynamics.

We discuss a connection between a generative model, called the diffusion model, and nonequilibrium thermodynamics for the Fokker-Planck equation, called stochastic thermodynamics. Based on the techniques of stochastic thermodynamics, we derive the speed-accuracy trade-off for the diffusion models, which is a trade-off relationship between the speed and accuracy of data generation in diffusion models. Our result implies that the entropy production rate in the forward process affects the errors in data generation. From a stochastic thermodynamic perspective, our results provide quantitative insight into how best to generate data in diffusion models. The optimal learning protocol is introduced by the conservative force in stochastic thermodynamics and the geodesic of space by the 2-Wasserstein distance in optimal transport theory. We numerically illustrate the validity of the speed-accuracy trade-off for the diffusion models with different noise schedules such as the cosine schedule, the conditional optimal transport, and the optimal transport.

After more than a century of concerted effort, physics still lacks basic principles of spontaneous self-organization. To appreciate why, we first state the problem, outline historical approaches, and survey the present state of the physics of self-organization. This frames the particular challenges arising from mathematical intractability and the resulting need for computational approaches, as well as those arising from a chronic failure to define structure. Then, an overview of two modern mathematical formulations of organization -- intrinsic computation and evolution operators -- lays out a way to overcome these challenges. Together, the vantage point they afford shows how to account for the emergence of structured states via a statistical mechanics of systems arbitrarily far from equilibrium. The result is a constructive path forward to principles of organization that builds on mathematical identification of structure.

A quantum thermal machine is an open quantum system that enables the conversion between heat and work at the micro or nano-scale. Optimally controlling such out-of-equilibrium systems is a crucial yet challenging task with applications to quantum technologies and devices. We introduce a general model-free framework based on Reinforcement Learning to identify out-of-equilibrium thermodynamic cycles that are Pareto optimal trade-offs between power and efficiency for quantum heat engines and refrigerators. The method does not require any knowledge of the quantum thermal machine, nor of the system model, nor of the quantum state. Instead, it only observes the heat fluxes, so it is both applicable to simulations and experimental devices. We test our method on a model of an experimentally realistic refrigerator based on a superconducting qubit, and on a heat engine based on a quantum harmonic oscillator. In both cases, we identify the Pareto-front representing optimal power-efficiency tradeoffs, and the corresponding cycles. Such solutions outperform previous proposals made in the literature, such as optimized Otto cycles, reducing quantum friction.

Active matter systems, from self-propelled colloids to motile bacteria, are characterized by the conversion of free energy into useful work at the microscopic scale. These systems generically involve physics beyond the reach of equilibrium statistical mechanics, and a persistent challenge has been to understand the nature of their nonequilibrium states. The entropy production rate and the magnitude of the steady-state probability current provide quantitative ways to do so by measuring the breakdown of time-reversal symmetry and the strength of nonequilibrium transport of measure. Yet, their efficient computation has remained elusive, as they depend on the system's unknown and high-dimensional probability density. Here, building upon recent advances in generative modeling, we develop a deep learning framework that estimates the score of this density. We show that the score, together with the microscopic equations of motion, gives direct access to the entropy production rate, the probability current, and their decomposition into local contributions from individual particles, spatial regions, and degrees of freedom. To represent the score, we introduce a novel, spatially-local transformer-based network architecture that learns high-order interactions between particles while respecting their underlying permutation symmetry. We demonstrate the broad utility and scalability of the method by applying it to several high-dimensional systems of interacting active particles undergoing motility-induced phase separation (MIPS). We show that a single instance of our network trained on a system of 4096 particles at one packing fraction can generalize to other regions of the phase diagram, including systems with as many as 32768 particles. We use this observation to quantify the spatial structure of the departure from equilibrium in MIPS as a function of the number of particles and the packing fraction.