温度和摩擦加速玻尔兹曼-吉布斯分布采样

Pareto and Boltzmann-Gibbs behaviors in a deterministic multi-agent system

A deterministic system of interacting agents is considered as a model for economic dynamics. The dynamics of the system is described by a coupled map lattice with near neighbor interactions. The evolution of each agent results from the competition between two factors: the agent's own tendency to grow and the environmental influence that moderates this growth. Depending on the values of the parameters that control these factors, the system can display Pareto or Boltzmann-Gibbs statistical behaviors in its asymptotic dynamical regime. The regions where these behaviors appear are calculated on th…

Machine learning algorithms based on generalized Gibbs ensembles

Machine learning algorithms often take inspiration from established results and knowledge from statistical physics. A prototypical example is the Boltzmann machine algorithm for supervised learning, which utilizes knowledge of classical thermal partition functions and the Boltzmann distribution. Recently, a quantum version of the Boltzmann machine was introduced by Amin, et. al., however, non-commutativity of quantum operators renders the training process by minimizing a cost function inefficient. Recent advances in the study of non-equilibrium quantum integrable systems, which never thermaliz…

深度为一的量子交替算子拟设作为近似Gibbs分布采样器

Depth One Quantum Alternating Operator Ansatz as an Approximate Gibbs Distribution Sampler

本研究数值调查了深度为一的QAOA从经典Ising模型定义的Boltzmann分布采样的能力，发现Grover混合器在高温下比标准X混合器更准确，两者均可作为近似采样器且效果取决于角度选择。

基于玻尔兹曼方程模拟复杂流体流动的壁面边界条件验证：动量输运与表面摩擦

Validation of wall boundary conditions for simulating complex fluid flows via the Boltzmann equation: Momentum transport and skin friction

本研究验证了玻尔兹曼方程壁面边界条件在多种流态下的有效性，发现高空间分辨率对预测流动不稳定性和动量输运至关重要，并首次直接求解玻尔兹曼方程计算了壁面湍流。

Multi-q Analysis of Image Patterns

This paper studies the use of the Tsallis Entropy versus the classic Boltzmann-Gibbs-Shannon entropy for classifying image patterns. Given a database of 40 pattern classes, the goal is to determine the class of a given image sample. Our experiments show that the Tsallis entropy encoded in a feature vector for different $q$ indices has great advantage over the Boltzmann-Gibbs-Shannon entropy for pattern classification, boosting recognition rates by a factor of 3. We discuss the reasons behind this success, shedding light on the usefulness of the Tsallis entropy.