克服相空间体积变化的一种新方法及哈密顿轨线的应用
A Novel Trick to Overcome the Phase Space Volume Change and the Use of Hamiltonian Trajectories with an emphasis on the Free Expansion
摘要：
我们扩展并成功地应用最近提出的微观非平衡态热力学研究膨胀/收缩过程。在这里，初始和最终微观状态的数量是不同的，所以它们不能通过唯一的哈密顿轨迹连接。这通常发生在相空间体积变化时，并且到目前为止还没有使用可以被反转以产生初始和最终微观状态之间的恒等映射的哈密顿轨迹来研究，因为哈密顿量中的参数被改变。我们提出了一个技巧，以克服这个障碍，重点是在一个孤立系，耗散工作的概念是不清楚的自由膨胀。技巧被证明是一致的，可以是非常有用的模拟。我们证明，耗散的是微观状态所做的内部微功的热力学平均值;这种微功不同于与真空的交换微功，后者会消失。我们还建立了微功是非负的自由膨胀，这是显着的，因为它的符号是不固定的一般过程。
英文摘要：
We extend and successfully apply a recently proposed microstate nonequilibrium thermodynamics to study expansion/contraction processes. Here, the numbers of initial and final microstates are different so they cannot be connected by unique Hamiltonian trajectories. This commonly happens when the phase space volume changes, and has not been studied so far using Hamiltonian trajectories that can be inverted to yield an identity mapping between initial and final microstates as the parameter in the Hamiltonian is changed. We propose a trick to overcome this hurdle with a focus on free expansion in an isolated system, where the concept of dissipated work is not clear. The trick is shown to be thermodynamically consistent and can be extremely useful in simulation. We justify that it is the thermodynamic average of the internal microwork done by a microstate that is dissipated; this microwork is different from the exchange microwork with the vacuum, which vanishes. We also establish that the microwork is nonnegative for free expansion, which is remarkable, since its sign is not fixed in a general process.
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