arXiv subjects

Liu Zhao

Publications and source records attributed to Liu Zhao.

At least 19 recordsLinked to original sources

arXiv2026

Geometric formulation for the relativistic kinetic theory of photons

We provide a geometric foundation for the kinetic theory of photons. Although the induced metric $\hat h$ on the light cone bundle $\Gamma_0^+$ is degenerate, which causes the corresponding volume element to vanish, we can still use a method similar to the Hodge dual to construct a volume element $\eta_{\Gamma_0^+}$ for the light cone bundle. Based on this geometric structure $(\Gamma^+_0,\eta_{\Gamma_0^+},\hat h)$, we establish the fully covariant Boltzmann equation for photons. More importantly, the volume element and the induced metric are linked in a nontrivial way, which allows the physical distributions to be defined consistently. This yields the corresponding hydrodynamic quantities and their divergences, which take the same form as in the case of massive particles.

gr-qc↗

arXiv2026

Statistical Mechanics of a Quantum Harmonic Oscillator with Folded Gaussian Frequency

A self-contained statistical-mechanics treatment of a single quantum harmonic oscillator is presented, whose frequency $\omega$ is drawn from a folded Gaussian distribution: $\omega=|\xi|$ with $\xi\sim\mathcal{N}(\mu,\sigma^2)$. The exact integral representations for the partition function, internal energy, free energy, heat capacity, and entropy are derived, and analytic approximations are given in two complementary limits---small variance ($\sigma\ll\mu$) via a cumulant expansion, and the zero-center case ($\mu=0$) via low-frequency asymptotic analysis. The model is extended to $N$ independent oscillators, where the heat capacity is shown to be extensive with self-averaging fluctuations $\propto N^{-1/2}$, and finally to a disordered oscillator lattice, where the folded-Gaussian kink at $\omega=0$ produces a soft-mode infrared tail. For a single isolated oscillator with $\mu=0$, both $C$ and $S$ vanish linearly at low $T$. In the lattice case, the van Hove factor converts this to a $T^d$ power law. The oft-quoted ``third-law violation'' for disordered phonons is here shown to be a spectral property---the absence of an energy gap and a power-law freeze-out---driven by the single-site distribution kink rather than by a genuine Lifshitz tail (which requires rare large-scale spatial fluctuations). The folded Gaussian thus serves as a minimal benchmark for soft-mode disorder thermodynamics.

cond-mat.stat-mech↗

arXiv2026

Unified Walking, Running, and Recovery for Humanoids via State-Dependent Adversarial Motion Priors

We propose a unified reinforcement learning framework that enables a single policy to perform walking, running, and fall recovery on the Unitree G1 humanoid robot, validated on physical hardware without any explicit mode-switching command at deployment. The framework extends Adversarial Motion Priors (AMP) by replacing the conventional global reference distribution with a state-dependent gate that routes each training transition to one of two discriminators: a dedicated recovery discriminator and a velocity-conditioned locomotion discriminator that jointly covers walking and running. The gate is defined by a single fixed threshold on projected gravity: the recovery discriminator is activated when body tilt exceeds approximately $37^\circ$ from vertical ($|g_z+1|>0.6$); otherwise the locomotion discriminator is used, with the normalized commanded velocity serving as a condition that selects the appropriate reference trajectory between walk and run clips. Only three LAFAN1 reference clips are required to regularize the complete behavior set. At deployment, a single frozen ONNX policy executes at 50\,Hz with no runtime mode logic; hardware experiments demonstrate successful recovery from both prone and supine falls and smooth walk-to-run transitions under the same controller.

cs.RO↗

arXiv2026

Large black holes at a finite distance: Quasi-local restricted phase space formalism

We extend the restricted phase space formalism for spherically symmetric black hole solutions of Einstein-Maxwell theory to the quasi-local regime, with the static observers located at a finite radial distance. The first law and Euler relation for the RN and RN-AdS black holes are proved to hold, but only with the inclusion of an extra pair of thermodynamic variables, {\em i.e.} the pressure $P$ and the area $A$ of the codimension-2 hypersurface on which the observers reside. For the RN black holes, the quasi-local behavior is analyzed in detail. It turns out that the RN black holes in the quasi-local description behaves significantly different from itself in the asymptotic description, but is extremely similar to the RN-AdS black holes in the asymptotic description, {\em e.g.} allowing for isocharge temperature-entropy phase transitions and lack of isovoltage temperature-entropy phase transitions. In the neutral limit, the Hawking-Page-like transitions appear in the quasi-local description which is absent in the asymptotic description. The quasi-local behavior of RN-AdS black holes is also briefly discussed, which is qualitatively identical to the asymptotic description with only quantitative differences.

gr-qc↗

arXiv2026

Learning Human-Like Badminton Skills for Humanoid Robots

Realizing versatile and human-like performance in high-demand sports like badminton remains a formidable challenge for humanoid robotics. Unlike standard locomotion or static manipulation, this task demands a seamless integration of explosive whole-body coordination and precise, timing-critical interception. While recent advances have achieved lifelike motion mimicry, bridging the gap between kinematic imitation and functional, physics-aware striking without compromising stylistic naturalness is non-trivial. To address this, we propose Imitation-to-Interaction, a progressive reinforcement learning framework designed to evolve a robot from a "mimic" to a capable "striker." Our approach establishes a robust motor prior from human data, distills it into a compact, model-based state representation, and stabilizes dynamics via adversarial priors. Crucially, to overcome the sparsity of expert demonstrations, we introduce a manifold expansion strategy that generalizes discrete strike points into a dense interaction volume. We validate our framework through the mastery of diverse skills, including lifts and drop shots, in simulation. Furthermore, we demonstrate the first zero-shot sim-to-real transfer of anthropomorphic badminton skills to a humanoid robot, successfully replicating the kinetic elegance and functional precision of human athletes in the physical world.

cs.RO↗

arXiv2025

MARG: MAstering Risky Gap Terrains for Legged Robots with Elevation Mapping

Deep Reinforcement Learning (DRL) controllers for quadrupedal locomotion have demonstrated impressive performance on challenging terrains, allowing robots to execute complex skills such as climbing, running, and jumping. However, existing blind locomotion controllers often struggle to ensure safety and efficient traversal through risky gap terrains, which are typically highly complex, requiring robots to perceive terrain information and select appropriate footholds during locomotion accurately. Meanwhile, existing perception-based controllers still present several practical limitations, including a complex multi-sensor deployment system and expensive computing resource requirements. This paper proposes a DRL controller named MAstering Risky Gap Terrains (MARG), which integrates terrain maps and proprioception to dynamically adjust the action and enhance the robot's stability in these tasks. During the training phase, our controller accelerates policy optimization by selectively incorporating privileged information (e.g., center of mass, friction coefficients) that are available in simulation but unmeasurable directly in real-world deployments due to sensor limitations. We also designed three foot-related rewards to encourage the robot to explore safe footholds. More importantly, a terrain map generation (TMG) model is proposed to reduce the drift existing in mapping and provide accurate terrain maps using only one LiDAR, providing a foundation for zero-shot transfer of the learned policy. The experimental results indicate that MARG maintains stability in various risky terrain tasks.

cs.RO↗

arXiv2025

SPEX: A Vision-Language Model for Land Cover Extraction on Spectral Remote Sensing Images

Spectral information has long been recognized as a critical cue in remote sensing observations. Although numerous vision-language models have been developed for pixel-level interpretation, spectral information remains underutilized, resulting in suboptimal performance, particularly in multispectral scenarios. To address this limitation, we construct a vision-language instruction-following dataset named SPIE, which encodes spectral priors of land-cover objects into textual attributes recognizable by large language models (LLMs), based on classical spectral index computations. Leveraging this dataset, we propose SPEX, a multimodal LLM designed for instruction-driven land cover extraction. To this end, we introduce several carefully designed components and training strategies, including multiscale feature aggregation, token context condensation, and multispectral visual pre-training, to achieve precise and flexible pixel-level interpretation. To the best of our knowledge, SPEX is the first multimodal vision-language model dedicated to land cover extraction in spectral remote sensing imagery. Extensive experiments on five public multispectral datasets demonstrate that SPEX consistently outperforms existing state-of-the-art methods in extracting typical land cover categories such as vegetation, buildings, and water bodies. Moreover, SPEX is capable of generating textual explanations for its predictions, thereby enhancing interpretability and user-friendliness. Code will be released at: https://github.com/MiliLab/SPEX.

cs.CV↗

arXiv2025

In-between Motion Generation Based Multi-Style Quadruped Robot Locomotion

Quadruped robots face persistent challenges in achieving versatile locomotion due to limitations in reference motion data diversity. To address these challenges, we introduce an in-between motion generation based multi-style quadruped robot locomotion framework. We propose a CVAE based motion generator, synthesizing multi-style dynamically feasible locomotion sequences between arbitrary start and end states. By embedding physical constraints and leveraging joint poses based phase manifold continuity, this component produces physically plausible motions spanning multiple gait modalities while ensuring kinematic compatibility with robotic morphologies. We train the imitation policy based on generated data, which validates the effectiveness of generated motion data in enhancing controller stability and improving velocity tracking performance. The proposed framework demonstrates significant improvements in velocity tracking and deployment stability. We successfully deploy the framework on a real-world quadruped robot, and the experimental validation confirms the framework's capability to generate and execute complex motion profiles, including gallop, tripod, trotting and pacing.

cs.RO↗

arXiv2024

Linear response in a charged gas in curved spacetime and covariant heat equation

We consider the linear response of a near-equilibrium charged relativistic gas in the presence of electromagnetic and gravitational field in a generic stationary spacetime up to the second order of relaxation time and calculate the tensorial kinetic coefficients introduced by the presence of the strong electromagnetic and/or gravitational field. Using the covariant transfer equations thus developed, a covariant heat equation governing the relativistic heat conduction is derived, which, in Minkowski spacetime, reduces into a form which is remarkably similar to the well-known Cattaneo equation but with a different sign in front of the second-order time derivative term. We also perform a comparative analysis on the different behaviors of our heat equation and the Cattaneo equation in Minkowski spacetime. Furthermore, the effect of gravity on the heat conduction predicted by our heat equation is illustrated around Schwarzschild black hole, which makes a sharp contrast to the Minkowski case.

gr-qc↗

arXiv2024

General Relativistic Fluctuation Theorems

Using the recently proposed covariant framework of general relativistic stochastic mechanics and stochastic thermodynamics, we proved the detailed and integral fluctuation theorems in curved spacetime. The time-reversal transformation is described as a transformation from the perspective of future-directed observer to that of the corresponding past-directed observer, which enables us to maintain general covariance throughout the construction.

gr-qc↗

arXiv2024

Fluctuation theorems in general relativistic stochastic thermodynamics

Based on the recently proposed framework of general relativistic stochastic mechanics [{\em J. Stat. Phys.}, 190:193, 2023; {\em J. Stat. Phys.}, 190:181, 2023] and stochastic thermodynamics [{\em SciPost Physics Core} 7, 082, 2024] at the ensemble level, this work focuses on general relativistic stochastic thermodynamics at the trajectory level. The first law of stochastic thermodynamics is reformulated and the fluctuation theorems are proved on this level, with emphasis on maintaining fully general covariance and on the choice of observers.

gr-qc↗

arXiv2023

Fluctuation Theorem on a Riemannian Manifold

Based on the covariant underdamped and overdamped Langevin equations with Stratonovich coupling to multiplicative noises and the associated Fokker-Planck equations on Riemannian manifold, we present the first law of stochastic thermodynamics on the trajectory level. The corresponding fluctuation theorems are also established, with the total entropy production of the Brownian particle and the heat reservoir playing the role of dissipation function.

cond-mat.stat-mech↗

arXiv2023

Thermodynamics for regular black holes as intermediate thermodynamic states and quasinormal frequencies

The thermodynamics for regular black holes (RBHs) is considered under the restricted phase space (RPS) formalism. It is shown that the RPS formalism seems to hold for RBHs, however, in order for the extensive thermodynamic parameters to be independent from each other, the RBHs need to be viewed as intermediate thermodynamic states in a larger class of black holes (BHs) which admit both regular and singular states. This idea is checked for several classes of BHs. In particular, for the electrically charged Hayward class BHs, it is shown that the regular states can either be thermodynamically stable or unstable, depending on the amount of charges carried by the BHs. The quasinormal frequencies for the Hayward class BHs are also analyzed, and it turns out that, even for the thermodynamically unstable regular states, the dynamic stability still holds, at least under massless scalar perturbations.

gr-qc↗

arXiv2023

General relativistic stochastic thermodynamics

Based on the recent work [1,2], we formulate the first law and the second law of stochastic thermodynamics in the framework of general relativity. These laws are established for a charged Brownian particle moving in a heat reservoir and subjecting to an external electromagnetic field in generic stationary spacetime background, and in order to maintain general covariance, they are presented respectively in terms of the divergences of the energy current and the entropy density current. The stability of the equilibrium state is also analyzed.

gr-qc↗

arXiv2023

A general relativistic kinetic theory approach to linear transport in generic hydrodynamic frame

In this study, we investigate the linear transport of neutral system within the framework of relativistic kinetic theory. Under the relaxation time approximation, we obtain an iterative solution to the relativistic Boltzmann equation in generic stationary spacetime. This solution provides a scheme to study non-equilibrium system order by order. Our calculations are performed in generic hydrodynamic frame, and the results can be reduced to a specific hydrodynamic frame by imposing constraints. As a specific example, we analytically calculated the covariant expressions of the particle flow and the energy momentum tensor up to the first order in relaxation time. Finally and most importantly, we present all 14 kinetic coefficients for a neutral system, which are verified to satisfy the Onsager reciprocal relation in a generic hydrodynamic frame and guarantee a non-negative entropy production in the frame where the first order conservation laws are restored.

gr-qc↗

arXiv2023

Relativistic stochastic mechanics II: Reduced Fokker-Planck equation in curved spacetime

The general covariant Fokker-Planck equations associated with the two different versions of covariant Langevin equation in Part I of this series of work are derived, both lead to the same reduced Fokker-Planck equation for the non-normalized one particle distribution function (1PDF). The relationship between various distribution functions is clarified in this process. Several macroscopic quantities are introduced by use of the 1PDF, and the results indicate an intimate connection with the description in relativistic kinetic theory. The concept of relativistic equilibrium state of the heat reservoir is also clarified, and, under the working assumption that the Brownian particle should approach the same equilibrium distribution as the heat reservoir in the long time limit, a general covariant version of Einstein relation arises.

cond-mat.stat-mech↗

arXiv2023

Gravito-thermal transports, Onsager reciprocal relation and gravitational Wiedemann-Franz law

Using the near-detailed-balance distribution function obtained in our recent work, we present a set of covariant gravito-thermal transport equations for neutral relativistic gases in a generic stationary spacetime. All relevant tensorial transport coefficients are worked out and are presented using some particular integration functions in $(\alpha,\zeta)$, where $\alpha = -\beta\mu$ and $\zeta =\beta m$ is the relativistic coldness, with $\beta$ being the inverse temperature and $\mu$ being the chemical potential. It is shown that the Onsager reciprocal relation holds in the gravito-thermal transport phenomena, and that the heat conductivity and the gravito-conductivity tensors are proportional to each other, with the coefficient of proportionality given by the product of the so-called Lorenz number with the temperature, thus proving a gravitational variant of the Wiedemann-Franz law. It is remarkable that, for strongly degenerate Fermi gases, the Lorenz number takes a universal constant value $L=\pi^2/3$, which extends the Wiedemann-Franz law into the Wiedemann-Franz-Lorenz law.

cond-mat.stat-mech↗

arXiv2023

Relativistic stochastic mechanics I: Langevin equation from observer's perspective

Two different versions of relativistic Langevin equation in curved spacetime background are constructed, both are manifestly general covariant. It is argued that, from the observer's point of view, the version which takes the proper time of the Brownian particle as evolution parameter contains some conceptual issues, while the one which makes use of the proper time of the observer is more physically sound. The two versions of the relativistic Langevin equation are connected by a reparametrization scheme. In spite of the issues contained in the first version of the relativistic Langevin equation, it still permits to extract the physical probability distributions of the Brownian particles, as is shown by Monte Carlo simulation in the example case of Brownian motion in $(1+1)$-dimensional Minkowski spacetime.

cond-mat.stat-mech↗