Can one measure the temperature of a curve?
Can one measure the temperature of a curve?
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可以测量曲线的温度吗？
DOI：
10.1007/bf00280431
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发表时间：
1986
影响因子：
2.5
通讯作者：
Michel Mendés
中科院分区：
文献类型：
--
作者：
Y. Dupain;T. Kamae;Michel Mendés
平面曲线的熵定义为与任意直线相交的点的个数。使熵最大化的吉布斯分布使人们能够定义曲线的温度。在0温度下，曲线减小为直线段。在高温下，曲线有些混乱，“表现得像一个完美的气体”。我们试图表明，热力学形式主义可以用于平面曲线的研究。我们讨论的曲线有有限的长度，不像Mandelbrot的分形曲线[1]，但我们觉得我们的数学方法离他不远。
The entropy of a plane curve is defined in terms of the number of intersection points with a random line. The Gibbs distribution which maximizes the entropy enables one to define the temperature of the curve. At 0 temperature, the curve reduces to a straight segment. At high temperature, the curve is somewhat chaotic and “behaves like a perfect gas”. We attempt to show that thermodynamic formalism can be used for the study of plane curves. The curves we discuss have finite length, unlike Mandelbrot's fractal curves [1], yet we feel our approach to the mathematics is not far from his.