Even when microscopic particle dynamics is purely mechanistic and thus reversible, the behavior of macroscopic systems composed of those particles is irreversible. In other words, effectively irreversible behavior emerges out of purely reversible dynamics when we do not observe all degrees of freedom of the detailed dynamics. But how can we find the irreversible macroscopic evolution equations when we only know the reversible microscopic equations? Using the so-called lack-of-fit reduction, which gives the reduced evolution as a sum of Hamiltonian and gradient dynamics, we reduce the purely Hamiltonian Kac–Zwanzig model to a set of irreversible evolution equations with no fitting parameters.

中文翻译：

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应用于 Kac-Zwanzig 模型的非平衡热力学失拟合减少

即使微观粒子动力学是纯粹机械的，因此是可逆的，由这些粒子组成的宏观系统的行为也是不可逆的。换句话说，当我们没有观察到详细动力学的所有自由度时，实际上不可逆的行为就会从纯粹可逆的动力学中出现。但是，当我们只知道可逆的微观方程时，如何才能找到不可逆的宏观演化方程呢？使用所谓的失拟约简（将约简演化作为哈密顿量和梯度动力学之和），我们将纯哈密顿量 Kac-Zwanzig 模型简化为一组没有拟合参数的不可逆演化方程。