AI 中文总结
该研究分析了孤立系统与恒温系统的吉布斯变分原理，结合柯尔莫哥洛夫方程阐明其与玻尔兹曼不可逆定理的关联，还通过实例推导自由能并分析伊辛模型相图。
AI 中文摘要
我们分析了与两类概率分布相关的吉布斯变分原理：（i）孤立系统的概率分布；（ii）恒温系统的概率分布。我们给出一个实例，说明如何利用吉布斯不等式推导自由能，并分析具有竞争相互作用的伊辛模型的相图。我们还回顾了玻尔兹曼不可逆定理，阐明其与吉布斯变分原理的关联，该关联通过概率分布演化的柯尔莫哥洛夫方程建立，此方程预测孤立系统的熵单调增加，而与热库接触的系统的自由能单调减小。
英文摘要
We analyze the Gibbs variational principles associated with the probability distributions of (i) an isolated system and (ii) a system at constant temperature. We give an example of using the Gibbs inequality to obtain the free energy and analyze the phase diagram of an Ising model with competing interactions. We also review the Boltzmann irreversible theorem, and show how it is connected to the Gibbs variational principles. This connection is established by using the Kolmogorov equation for the evolution of the probability distribution, which predicts a monotonic increase of entropy for an isolated system, and a decrease of the free energy for a system in contact with a thermal reservoir.
Journal refRevista Brasileira de Ensino de Física, vol. 48, e20260079 (2026)
