标题： 负温度下的H定理：有界随机交换模型 显示英文标题

标题： H-theorem at negative temperature: the random exchange model with bounds

摘要： 随机交换动力学模型被广泛用于描述大相互作用系统的保守动力学。 由于其简单性和普遍性，它们在多个领域非常受欢迎，从统计力学到生物物理和经济学。 在这里，我们研究了一个版本，在该版本中引入了全局守恒量的个体份额的限制。 我们通过分析证明，这种动力学允许具有种群反转的稳态，如果守恒量具有能量的物理意义，则由负绝对温度的玻尔兹曼统计描述。 因此，所提出的模型为研究向负温度状态热化提供了一个有利的系统。 首先，通过检查详细平衡条件来验证稳态的真实平衡性质。 然后，证明了一个H定理，确保通过玻尔兹曼熵的单调增加达到这种平衡条件。 我们还提供了分析和数值证据，表明与系统接触的大入侵者会热化，这表明了一种设计负温度热浴的实际方法。 显示英文摘要

摘要： Random exchange kinetic models are widely employed to describe the conservative dynamics of large interacting systems. Due to their simplicity and generality, they are quite popular in several fields, from statistical mechanics to biophysics and economics. Here we study a version where bounds on the individual shares of the globally conserved quantity are introduced. We analytically show that this dynamics allows stationary states with population inversion, described by Boltzmann statistics at negative absolute temperature if the conserved quantity has the physical meaning of an energy. The proposed model provides therefore a privileged system for the study of thermalization toward a negative temperature state. First, the genuine equilibrium nature of the stationary state is verified by checking the detailed balance condition. Then, an H-theorem is proven, ensuring that such equilibrium condition is reached by a monotonic increase of the Boltzmann entropy. We also provide analytical and numerical evidence that a large intruder in contact with the system thermalizes, suggesting a practical way to design a thermal bath at negative temperature.