论文标题
非平衡分子动力学，分形相位分布，cantor集和涉及两个可压缩面包师图的信息尺寸的难题
Nonequilibrium Molecular Dynamics, Fractal Phase-Space Distributions, the Cantor Set, and Puzzles Involving Information Dimensions for Two Compressible Baker Maps
论文作者
论文摘要
确定性和时间可转移的非平衡分子动力学模拟通常会产生“分形” [分数维]相位空间分布。由于这些分布及其时间转换的双胞胎的相体积为零，因此稳定的吸引子“向前”和不稳定的（不可观察）驱虫剂时，这些模拟与第二种热力学定律一致。这些相同的可逆性和稳定性也可以在可压缩的面包师图中或等效的随机步行中找到，从而激发了他们的仔细研究。我们用三个示例说明了这些想法：cantor-stet地图和两个线性可压缩的面包师地图，n2 $（q，p）$和n3 $（q，p）$。从顺序映射估算的两个贝克地图的信息维度同意，而次迭代的次要映射尺寸却没有，估计值取决于地图的非平衡稳态方法的细节。
Deterministic and time-reversible nonequilibrium molecular dynamics simulations typically generate "fractal" [ fractional-dimensional ] phase-space distributions. Because these distributions and their time-reversed twins have zero phase volume, stable attractors "forward in time" and unstable (unobservable) repellors when reversed, these simulations are consistent with the Second Law of Thermodynamics. These same reversibility and stability properties can also be found in compressible Baker Maps, or in their equivalent random walks, motivating their careful study. We illustrate these ideas with three examples: a Cantor-Set Map and two linear compressible Baker Maps, N2$(q,p)$ and N3$(q,p)$. The two Baker Maps' Information dimensions estimated from sequential mappings agree while those from pointwise iteration do not, with the estimates dependent upon details of the approach to the maps' nonequilibrium steady states.
