In order to support the introduction of this basic principle, Boltzmann put forward the so-called ergodic hypothesis, which holds that a phase trajectory can run all over (or fill) the whole energy surface. Later, some people put forward the quasi-ergodic hypothesis that a phase trajectory can arbitrarily approach any point on the energy surface. However, the mathematical research points out that the above ergodic hypothesis cannot be established, and the quasi ergodic hypothesis is not enough to guarantee "phase average = time average". Therefore, the future research on the mathematical basis of statistical mechanics will focus on the condition of "phase average = time average", and the system that meets this condition is called ergodicity or ergodicity. Since 1930s, marked by the work of many mathematicians, such as g d boekhoff, J von Neumann and α я Qin Xin, ergodicity research has become an important branch of mathematics.
Teaching reflection on finding the greatest common factor 1
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