标题： 共享费用公平性的统计物理观点：酒吧账单类比 显示英文标题

标题： A Statistical Physics perspective on fairness in shared expenses: The bar bill analogy

摘要： 在个体消费量不同的社交场合，如共进餐食或酒吧聚会，平均分摊总账单往往会产生出人意料的公平结果。 在本工作中，我们开发了一个统计物理框架，通过将个体消费建模为来自现实分布（特别是伽马分布）的随机变量，来解释这种涌现的公平性。 引入一个类似玻尔兹曼的加权因子，我们推导了在经济或社会惩罚约束下的配分函数、平均消费、方差和熵的精确解析表达式。 使用Marsaglia-Tsang算法进行的数值模拟以高精度验证了分析结果。 通过将个体消费与规范系综中理想气体粒子能量之间的直接类比，我们展示了大数定律、相互补偿以及惩罚引起的有效有序性如何共同使均等费用分摊在统计上具有鲁棒性和可预测性。 这些发现表明，看似非正式的社会惯例实际上建立在支配热力学系统集体行为的基本原理之上，突显了统计物理的跨学科力量。 显示英文摘要

摘要： In social contexts where individuals consume varying amounts, such as shared meals or bar gatherings, splitting the total bill equally often yields surprisingly fair outcomes. In this work, we develop a statistical physics framework to explain this emergent fairness by modeling individual consumption as stochastic variables drawn from a realistic distribution, specifically the gamma distribution. Introducing a Boltzmann-like weighting factor, we derive exact analytical expressions for the partition function, average consumption, variance, and entropy under economic or social penalization constraints. Numerical simulations, performed using the Marsaglia-Tsang algorithm, confirm the analytical results with high precision. Drawing a direct parallel between individual consumption and ideal gas particle energy in the canonical ensemble, we show how the law of large numbers, mutual compensation, and the effective ordering induced by penalization combine to make equal cost-sharing statistically robust and predictable. These findings reveal that what appears to be an informal social convention is, in fact, grounded in the same fundamental principles that govern the collective behavior of particles in thermodynamic systems, highlighting the interdisciplinary power of statistical physics.