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Irreversible statistical mechanics from reversible motion: Q2R automata

机译：来自可逆运动的不可逆统计力学：Q2R自动机

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摘要

Q2R cellular automata are a nice pedagogical example for addressing a century-old question discussed at the 20th IUPAP Statistical Physics Conference in Paris last July: How is thermodynamic-irreversibility, as seen in entropy increase, compatible with microscopic reversibility, as in Newton's equations of motion? The Boltzmann-Zermelo argument says that the times for returning to the low-entropy initial state of a large system are far longer than the age of the universe. How can we test this assertion? Molecular dynamics in its usual form is inadequate to address this question, since arithmetic rounding errors as well as discretization of space and time preclude return to the exact initial configuration. Monte Carlo simulations of Ising models avoid such errors but require random numbers and are therefore not reversible in the usual sense. The Q2R update rules of cellular automata for microcanonical Ising models are reversible and the system returns exactly to the initial configuration after an exponentially long time. Computer simulation of Q2R cellular automata help us to understand some very old fundamental problems. This property will be reviewed, as well well as unexplained critical exponents obtained in large-scale simulations.
机译：Q2R元胞自动机是解决去年7月在巴黎举行的第20届IUPAP统计物理会议上讨论的一个世纪之久的问题的很好的教学法示例：如熵增所示，热力学不可逆性如何与微观可逆性兼容，如牛顿方程运动？ Boltzmann-Zermelo的论点说，返回大系统的低熵初始状态的时间远远长于宇宙的寿命。我们如何测试这个断言？通常的形式的分子动力学不足以解决这个问题，因为算术四舍五入误差以及空间和时间的离散化都无法返回到精确的初始构型。伊辛模型的蒙特卡洛模拟避免了此类错误，但需要随机数，因此在通常意义上是不可逆的。微经典Ising模型的细胞自动机的Q2R更新规则是可逆的，并且在经过一段指数的时间后，系统会完全返回到初始配置。 Q2R元胞自动机的计算机仿真有助于我们理解一些非常古老的基本问题。将审查此属性，以及在大规模模拟中获得的无法解释的临界指数。

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