Experimental investigations of stochastic thermodynamics

大约150年前，麦克斯韦第一次提出了这样一个问题：当一个“手指整洁的生物”--一个恶魔--利用信息从热量中做功时，会发生什么？ 热力学第二定律应该禁止这种情况，但怎么做呢？ 这个问题困扰了物理学家，并引发了长达世纪的争论。一年前，在我的实验室里，我们做了一个明确的测量，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，而擦除信息需要消耗尽可能多的能量。 这里提出的工作追求这些想法的情况下，系统是不平衡的。 一个重要的目标是能够测量函数的形式，该函数描述了一个系统的熵。 有人提出，但从未直接测试过，香农熵扮演了这个角色。 这个函数表面上看起来像是世纪标准的吉布斯-玻尔兹曼熵表达式，但它适用于不平衡状态。我提出的工作利用了反馈陷阱，这是我和我的团队在我目前的发现资助期间开发的一种高精度仪器。我们将继续改进这个陷阱，并利用它模拟任意时间依赖势（甚至不是来自势的力场）的能力，进行一系列位于非平衡统计物理学、控制和信息论交叉点的实验。 项目包括最佳控制如何在有限的时间内完成一项任务（如擦除信息），同时做尽可能少的工作;昂萨格系数及其对称性（和缺乏）的周期性调制的电位;和推断，可以突然改变更多的信息是收购的尤里卡时刻。 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，而是可以通过明显的跳跃进行的。我们还将探索在更复杂的环境中的扩散，例如靠近墙壁。 微妙的事情发生运动在不同的方向变得不同，例如。 我们将在三种情况下研究这个问题：磁珠、棒状粒子和DNA（它像球体一样球状，但在靠近墙壁时会变形）。在所有这些实验中，总的目标是为21世纪建立一种科学，就像热力学是18世纪的蒸汽机一样。 这样的科学将解释在小系统中什么是可能的，什么是不可能的，以及如何实现最大的可能效率。 它将结合微观和纳米尺度的技术进步，了解机器，电机和其他设备如何在热波动巨大但仍然必须做出可靠决策的环境中工作。 这些问题是我们理解生物学和生命以及小规模工程的基础。 他们提供了宝贵的机会，为加拿大的技术和未来的就业机会在各级培训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.********