Cynosure对《Statistical Mechanics》的笔记(1)

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samplingas an ingenious method for evaluating integrals which are unsolvable byother methods。
The explicit formula for the binomial distribution (eqn (1.47)) is inconvenient for practical evaluation because of the large numbers enteringthe coefficients in eqn (1.48). It is better to relate the probability distribution π for N + 1 trials to that for N trials:
Latin 'convolvere': to roll together, fold together, or intertwine.
为何使用平方而不是绝对值来衡量差异：The additivity of variances for the sum of independent random variablesis of great importance. No analogous relation exists for the mean absolute deviation.
The chaos in the hard-sphere model has its origin in the negativecurvature of the spheres’ surfaces, which magnifies tiny differences inthe trajectory at each pair collision and causes serious rounding errors in computations and humbling experiences at the billiard table (seeFig. 2.6).