关键词: 熵守恒, 熵增, 理想气体, 速度量子化, 速度分辨率, 最大熵

Abstract: The entropy of microscopic configurations of a classical ideal gas system located on a one-dimensional ring is investigated. It is verified that the distribution of particles on the ring becomes more and more uniform，and the positional entropy increases with time toward the maximum value，while the total entropy (contributed by positional uncertainty and velocity uncertainty) is conserved in the rigorous mathematical sense. The velocities of particles which are passing through the same position at the same time become more and more quantized，and the gap between adjacent discrete velocity values gradually reduces to zero as time increases. This quantization property means that，as the velocity resolution limit of an observer must be finite in the sense of physical measurement，the measured entropy of microscopic configurations must be increasing with time. This simple system is helpful for understanding the second law of thermodynamics.

Key words: entropy conservation, entropy increase, classical ideal gas, quantization of velocity, velocity resolution limit, maximum entropy