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Boltzmann accomplished the feat of showing that the second law of thermodynamics is only a statistical fact. The gradual disordering of energy is analogous to the disordering of an initially ordered [[pack of cards]] under repeated shuffling, and just as the cards will finally return to their original order if shuffled a gigantic number of times, so the entire universe must some-day regain, by pure chance, the state from which it first set out. (This optimistic coda to the idea of the dying universe becomes somewhat muted when one attempts to estimate the timeline which will probably elapse before it spontaneously occurs.)<ref>"[[Collier's Encyclopedia]]", Volume 19 Phyfe to Reni, "Physics", by David Park, p. 15</ref> The tendency for entropy increase seems to cause difficulty to beginners in thermodynamics, but is easy to understand from the standpoint of the theory of probability. Consider two ordinary [[dice]], with both sixes face up. After the dice are shaken, the chance of finding these two sixes face up is small (1 in 36); thus one can say that the random motion (the agitation) of the dice, like the chaotic collisions of molecules because of thermal energy, causes the less probable state to change to one that is more probable. With millions of dice, like the millions of atoms involved in thermodynamic calculations, the probability of their all being sixes becomes so vanishingly small that the system ''must'' move to one of the more probable states.<ref>"Collier's Encyclopedia", Volume 22 Sylt to Uruguay, Thermodynamics, by Leo Peters, p. 275</ref> However, mathematically the odds of all the dice results not being a pair sixes is also as hard as the ones of all of them being sixes{{Citation needed|date=January 2019}}, and since statistically the [[data]] tend to balance, one in every 36 pairs of dice will tend to be a pair of sixes, and the cards -when shuffled- will sometimes present a certain temporary sequence order even if in its whole the deck was disordered.

Boltzmann accomplished the feat of showing that the second law of thermodynamics is only a statistical fact. The gradual disordering of energy is analogous to the disordering of an initially ordered [[pack of cards]] under repeated shuffling, and just as the cards will finally return to their original order if shuffled a gigantic number of times, so the entire universe must some-day regain, by pure chance, the state from which it first set out. (This optimistic coda to the idea of the dying universe becomes somewhat muted when one attempts to estimate the timeline which will probably elapse before it spontaneously occurs.)<ref>"[[Collier's Encyclopedia]]", Volume 19 Phyfe to Reni, "Physics", by David Park, p. 15</ref> The tendency for entropy increase seems to cause difficulty to beginners in thermodynamics, but is easy to understand from the standpoint of the theory of probability. Consider two ordinary [[dice]], with both sixes face up. After the dice are shaken, the chance of finding these two sixes face up is small (1 in 36); thus one can say that the random motion (the agitation) of the dice, like the chaotic collisions of molecules because of thermal energy, causes the less probable state to change to one that is more probable. With millions of dice, like the millions of atoms involved in thermodynamic calculations, the probability of their all being sixes becomes so vanishingly small that the system ''must'' move to one of the more probable states.<ref>"Collier's Encyclopedia", Volume 22 Sylt to Uruguay, Thermodynamics, by Leo Peters, p. 275</ref> However, mathematically the odds of all the dice results not being a pair sixes is also as hard as the ones of all of them being sixes{{Citation needed|date=January 2019}}, and since statistically the [[data]] tend to balance, one in every 36 pairs of dice will tend to be a pair of sixes, and the cards -when shuffled- will sometimes present a certain temporary sequence order even if in its whole the deck was disordered.

玻尔兹曼完成了证明热力学第二定律只是一个统计事实的壮举。能量的逐渐无序化类似于一叠最初有序排列的卡牌重复洗牌过程中变得无序，也正如经历了无数次洗牌而重归初始有序状态的卡牌一样，我们的宇宙最终将在某一时刻回到最初的状态。（当人们试图估计宇宙正在消亡的时间线时，这种乐观的结论就显得有些平淡了，因为时间线很可能在它自然发生之前就已经过去了。）熵增加的趋势似乎对初学热力学的人们造成困难，但从概率论的观点出发就很容易理解。考虑两个普通的骰子，都是正面朝上的。摇骰子后，发现这两个6面朝上的概率很小(1 / 36)；因此，我们可以说，骰子的随机运动，就像分子由于热能的混乱碰撞，导致概率较小的状态变为概率较大的状态。有了数以百万计的骰子，就像热力学计算中数以百万计的原子一样，它们全部为6的概率变得如此之小，以至于系统必须移动到一个更可能的状态。然而，数学上所有骰子结果的几率不是一对6也一样硬的都是6，由于统计数据趋于平衡，每36对骰子会一双6，而洗过的牌有时会呈现出某种临时的顺序，即使整个牌是无序的。

玻尔兹曼完成了证明热力学第二定律只是一个统计事实的壮举。能量的逐渐无序化类似于一叠最初有序排列的卡牌重复洗牌过程中变得无序，也正如经历了无数次洗牌而重归初始有序状态的卡牌一样，我们的宇宙最终将在某一时刻回到最初的状态。（当人们试图估计宇宙正在消亡的时间线时，这种乐观的结论就显得有些平淡了，因为时间线很可能在它自然发生之前就已经过去了。）熵增加的趋势似乎对初学热力学的人们造成困难，但从概率论的观点出发就很容易理解。考虑两个普通的骰子，都是正面朝上的。摇骰子后，发现这两个6面都朝上的概率很小(1 / 36)；因此，我们可以说，骰子的随机运动，就像分子由于热能的混乱碰撞，会导致系统从概率较小的状态变为概率较大的状态。数以百万计的骰子，就像热力学计算中数以百万计的原子一样，它们全部为6的概率变得如此之小，以至于系统必须移动到一个更可能的状态。然而，数学上出现所有骰子结果都是6或者都不是6的几率都很小，由于统计数据会趋于平衡，每36对骰子会有一对6出现，而洗过的牌有时会呈现出某种临时的顺序，即使整个牌是无序的。

==获奖经历与荣誉==

==获奖经历与荣誉==