Experimental investigations of stochastic thermodynamics

大约150年前，麦克斯韦第一次问到，当“灵巧的指状生物”--恶魔--使用信息从热量中提取功时，会发生什么。热力学第二定律应该禁止这种情况，但如何做到呢？一个多世纪以来，这个问题一直困扰着物理学家，并引发了争论。一年前，在我的实验室里，我们进行了一项决定性的测量，证实了50年前提出的一个假设：麦克斯韦恶魔需要擦除信息，擦除信息需要消耗尽可能多的能量。这里提出的工作将这些想法推广到系统失衡的情况。一个重要的目标是能够测量描述系统不平衡的熵的函数的形式。有人提出，香农熵扮演着这一角色，但从未进行过直接测试。这个函数表面上看起来像19世纪吉布斯-玻尔兹曼关于熵的标准表达式，但它的应用超出了平衡。 我提出的这项工作利用了反馈陷阱，这是我和我的团队在我目前的发现拨款期间开发的一种高精度仪器。我们将继续改进这一陷阱，并将利用其模拟任意含时势(甚至不是来自势的力场)的能力来执行一系列位于非平衡统计物理、控制和信息论的交叉点的实验。项目包括最优控制--如何在完成尽可能少的工作的同时，在有限的时间内完成一项任务(例如擦除信息)；周期性调制电位的Onsager系数及其对称性(及其缺失)；以及随着获得更多信息而突然发生变化的推论--尤里卡矩。我们将检验这样一种观点，即学习不一定是一个缓慢、稳定的过程，而是可以以明显的跳跃进行。 我们还将探索在更复杂的环境中的扩散，例如靠近墙的环境。微妙的事情发生了--例如，运动在不同的方向上变得不同。我们将在三个环境中观察这一点：磁珠、棒状粒子和DNA(它像球体一样球状，但可以在墙壁附近变形)。 在所有这些实验中，总体目标是在21世纪建立热力学对于18世纪蒸汽机的那种科学。这样的科学将解释在小型系统中什么是可能的，什么是不可能的，以及如何实现最大可能的效率。它将结合微米和纳米级技术的进步，了解机器、电机和其他设备如何在热波动巨大但仍必须做出可靠决定的环境中工作。这些问题奠定了我们对生物学、生命以及小规模工程学的理解。它们提供了宝贵的机会，为加拿大未来的技术和工作培训各级HQP。

Nearly 150 years ago, Maxwell first asked what happens when a “neat fingered being” - a demon - uses information to extract work from heat. The Second Law of Thermodynamics should forbid this, but how? The question has galled physicists and provoked debate for over a century. One year ago in my laboratory, we made a definitive measurement that confirms a hypothesis proposed 50 years ago: that Maxwell demons need to erase information and that erasing information requires dissipating as much energy as is gained. The work proposed here pursues these ideas to cases where systems are out of equilibrium. One important goal is to be able to measure the form of the function that describes the entropy of a system out of equilibrium. It has been proposed, but never directly tested, that the Shannon entropy plays this role. The function superficially looks like the standard 19th century Gibbs-Boltzmann expression for the entropy but applies out of equilibrium. The work I propose takes advantage of the feedback trap, a device that my group and I developed into a high-precision instrument during my current Discovery Grant. We will continue to improve this trap and will also take advantage of its abilities to mimic an arbitrary time-dependent potential (or even a force field that does not come from a potential) to carry out a range of experiments that lie at the intersection of nonequilibrium statistical physics, control, and information theory. Projects include optimal control - how to carry out a task (such as erasing information) in a finite time while doing the least possible amount of work; Onsager coefficients and their symmetries (and lack thereof) for periodically modulated potentials; and inferences that can suddenly change as more information is acquired - the Eureka moment. We will test the idea that learning need not be a slow, steady process but can proceed by distinct jumps. We will also explore diffusion in more complex settings, such as near a wall. Subtle things happen - motion becomes different in different directions, for example. We will look at this in three settings: a magnetic bead, a rod-shaped particle, and DNA (which balls up like a sphere but can deform near a wall). In all of these experiments, the overall goal is to establish, for the 21st century, the kind of science that thermodynamics was to 18th century steam engines. Such a science would explain what is possible in small systems, what is not, and how to achieve the greatest possible efficiencies. It will marry the advances in technology at micro- and nanoscales with an understanding of how machines, motors, and other devices work in a setting where thermal fluctuations are huge but where reliable decisions still must be made. These are questions that underlie our understanding of biology and life as well as engineering at small scales. They provide valuable opportunities to train HQP at all levels for Canada’s technologies and jobs of the future.