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So the triple point is liquid solid, gas, all in equilibrium.
气态，固态，三相平衡,你可能会想。
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So it's going to shoot up until the internal pressure and the external pressure are in equilibrium.
活塞将上,移直到内外,压强达到平衡。
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We find that profit in equilibrium is equal to what?
我们发现均衡下的利润为什么呢
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Nobody can see the interest rate-- why the interest rate's at the level it is in the market-- because nobody can see all these individuals; but that's why the interest rate gets determined and is in equilibrium.
没有人能知道,为什么市场利率会是现在的结果,因为没有人能知道其他人的想法,但市场利率就是这样确定并达到均衡
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So, then we go to thermodynamics and chemical equilibrium, and this is really about chemical reactions -- weather a reaction will go, will it be spontaneous, if there an equilibrium, what direction will the reaction be shifted in.
然后我们要讲到热力学和化学平衡,这都和化学反应有关，一个反应是否能发生,是不是能自发反应，如果存在化学平衡，它会朝什么方向移动。
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But if the system is in equilibrium, none of those states has lower enthalpy.
但是如果系统处于平衡态，所有其他的态都不可能具有更低的自由焓。
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It's reversible, that means that p external, equals p. I'm doing it very slowly so that I'm always in equilibrium between the external pressure and the internal pressure so I can go back and forth.
我都可以不损失能量，而把过程逆向进行,整个过程中的,每一步都保持平衡,现在我们来分别。
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So it applies to macroscopic systems that are in equilibrium, and how to go from one equilibrium state to another equilibrium state, and it's entirely empirical in its foundation.
因此，热力学研究的是平衡态的宏观系统,以及如何从,一个平衡态过渡到另一个平衡态，它完全是建立在经验的基础上的。
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p1 I said let's do this slowly enough that this p1 is in equilibrium with this p1, but not so slowly that this pressure is equivalent to that pressure.
我曾说过我们足够慢地使这边的1,与这边的p1平衡，但是没有慢到,这里的压强等于这里的压强。
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Even though these best responses are pretty complicated it turns out that there's only one Nash Equilibrium in this game.
虽然最佳对策是很复杂的,在这个博弈中却只有一个纳什均衡
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In other words, if we don't have to worry about entropy or volume equilibrium is achieved when energy is at a minimum.
换句话说，如果我们不担心熵,和体积的平衡,那么能量就得是最小的。
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And in this game if they keep on doing that, it's going to drag them back to Nash Equilibrium.
这个博弈,如果他们一直这样做,最终会达到纳什均衡的状态
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Every time you do the experiment T in equilibrium with the heat bath at T, v2 you'll get the same p2 and V2.
与热库相接触的每次实验中,达到热平衡后的温度都是，压强都是p2，体积都是。
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And the triple point of water is 16K that temperature and pressure - there's a unique temperature and pressure where water exists in equilibrium between the liquid phase, the vapor phase, and the solid phase.
与水的三相点,我们定义它为273。,水的三相点,是一个特定的温度和压强,可以使水的液态，气态和固态三相共同达到平衡，三相点是液态。
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If delta G equals zero, then we're already in equilibrium.
如果dG等于零，我们就处于平衡态。
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And in the end, when it's at equilibrium, and you look and you'd make a measurement, right, you could do spectroscopy.
当他处于平衡状态的时候，你可以做测量，比方说做光谱分析。
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So what we want to do is we want to figure out what the Nash Equilibrium looks like in this market.
我们想要做的是,找出这个市场的纳什均衡是什么
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In those cases, though, you'd have quite a reasonable equilibrium, spontaneously that is there would be a lot of reaction that went if you simply started under practical conditions and let it go.
你也会得到平衡，尽管在这种情况下你得到了一个,自发的，合理的平衡,这是在正常条件下进行的,许多化学反应的情况。
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So if I get rid of these arrows, there's no heat flowing because they're in thermal equilibrium, then I can't have an arrow here.
所以如果我擦去这些箭头，没有热流存在,因为它们处于热平衡，那么这里也不能存在一个箭头。
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If I've got a gas in a container, the pressure of the gas has to be the same everywhere in the container, otherwise it's not equilibrium.
如果把气体装进容器里，容器内各处气体的压强,应该是一样的，否则它就不是平衡的。
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So I just want to use that again and again, starting from that, for various different sorts of conditions andderive the criterion for equilibrium in each set of conditions.
所以我将会一遍又一遍地使用这个公式，从这个公式出发，在各种条件了,推导出,任意条件下的平衡条件。
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We're going to find other properties that do care about the history of the system like work, that you put in the system, or heat that you put in the system, or some other variables But you can't use those to define the equilibrium state.
我们还会发现其他一些,与系统的历史有关的性质,比如你对系统做的功，或者你向系统传递的热量，或其他的变量,但你不能用它们,来定义平衡态。
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And knowing now how to calculate these free energies especially the Helmholtz and the Gibbs free energies,that's what's going to guide us in really calculating quantitatively, OK, where will equilibrium lie.
知道如何计算,这些自由能,尤其是亥姆赫兹和吉布斯自由能之后,这些数值计算就能告诉我们，平衡态到底是什么样子。
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In other words, we need criteria for equilibrium under more general conditions than the ones that we've dealt with so far, than the one set of conditions that we've dealt with so far, which is isolated system.
换句话说,相比我们目前为止,考虑和处理的问题，我们需要更一般条件下平衡的判据,我们目前，只考虑了孤立系统。
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As an exercise in finding Nash Equilibrium, by this stage in the course most of you are looking at that saying, that wasn't hard.
作为寻找纳什均衡的一个练习,在此阶段,你们中的大多数人都会说,那不难
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So this is the total quantity produced on this equilibrium, in this Cournot Nash Equilibrium.
这就是在古诺博弈中的,纳什均衡
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Is there a Nash Equilibrium In which one and only one candidate stands?
有且只有一个,候选人参选是纳什均衡吗
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Of course there are lots of states that would have maybe local pockets of one substance in excess and another substance in excess somewhere else In other words, there would be lots of states nearby to the equilibrium state.
当然，我们有很多的态,这些态中，某些位置被一种气体完全占据,另外一些位置被另一种气体完全占据,换句话说,在平衡态附近有很多的态。
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The reason is that the best response for Firm 1, So it turns out it's pretty to check that this is the only Nash Equilibrium in the game.
因为公司1的最佳对策,所以很容易验证,这是此博弈中唯一的纳什均衡
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Well at the end of the day we learned that in the Cournot Equilibrium, things were, as we perhaps might have anticipated-- things sat naturally between the extreme cases.
在上次课结束时,我们学到了,在古诺均衡下,多少如我们所预料的,事情很自然地处于极端情况之间
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