The efficiency of classical heat engines is bounded by the Carnot efficiency leading to vanishing power. Efficiency at maximum power is often related to the Curzon–Ahlborn efficiency. As a paradigm for a periodic stochastic heat engine, a Brownian particle in a harmonic potential is sequentially coupled to two heat baths. For a simple steady-state heat engine, a two-state model coupled permanently to two heat baths leads to transport against an external force or against an imposed electrochemical potential. Affinities and Onsager coefficients in the linear response regime are determined. The identification of exchanged heat in the presence of particle transport is shown to be somewhat ambiguous.

Spanish physicist Maria Lluïsa Canut (1924–2005) specialized in the application of X-ray diffraction to the determination of molecular crystal structures, a field at the intersection of crystallography and quantum mechanics. She completed her PhD at the University of Barcelona under the supervision of José Luís Amorós (1920–2001). After becoming a couple, the two developed joint research projects. In the 1960s, they moved to Southern Illinois University, where she notably built computing programs to analyze molecular structures from X-ray diffraction patterns. In parallel, Canut became involved in the struggle for pay parity at the university. This participation in the US second feminist wave sparked her interest in science policy. After the couple moved back to Madrid in the 1970s, Amorós continued with crystallographic research, whereas Canut became involved in American–Spanish scientific cooperation and computing systems applied to university libraries. This chapter analyzes Canut’s scientific contributions against the backdrop of her gender and across the changing contexts of her career, including the role played by scientific couples in the research enterprise.

Take an electric charge and shake it and it will produce light. The purpose of this chapter is to explain how this works.

The Hamiltonian plays the starring role in the standard formulation of quantum mechanics. But, back in the classical world, there are two equivalent ways to write down a theory, one using the Hamiltonian and the other using the Lagrangian. It’s natural to wonder if there might also be another formulation of quantum mechanics, where things are written in terms of the Lagrangian. Happily, there is. And it’s lovely. Its called the path integral

The main ideas are introduced in a historical context. Beginning with phase retrieval and ending with neural networks, the reader will get a sense of the book’s broad scope.

There are four forces in our universe. Two act only at the very smallest scales and one only at the very biggest. For everything inbetween, there is electromagnetism. The theory of electromagnetism is described by four gloriously simple and beautiful vector calculus equations known as the Maxwell equations. These are the first genuinely fundamental equations that we meet in our physics education and they survive, essentially unchanged, in our best modern theories of physics. They also serve as a blueprint for what subsequent laws of physics look like.

This textbook takes us on a tour of the Maxwell equations and their many solutions. It starts with the basics of electric and magnetic phenomena and explains how their unification results in waves that we call light. It then describes more advanced topics such as superconductors, monopoles, radiation, and electromagnetism in matter. The book concludes with a detailed review of the mathematics of vector calculus.

Newtons laws of motion are not the last word in classical mechanics. In the 250 years after Newton, physicists and mathematicians found ways to reformulate classical mechanics, providing powerful tools to solve problems but, equally as importantly, giving us a new perspective on the laws that govern our universe. This chapter takes the first step in this direction. We will introduce the wonderful principle of least action, a simple rule that underlies all known laws of physics. This will give us new insights, not least the wonderful Noethers theorem, relating symmetries to conservation laws.

Beginning with linear programming and ending with neural network training, this chapter features seven applications of the divide-and-concur approach to solving problems with RRR.

In 1925, as matrix mechanics was taking shape, Lucy Mensing (1901−1995), who earned her PhD with Lenz and Pauli in Hamburg, came to Göttingen as a postdoc. She was the first to apply matrix mechanics to diatomic molecules, using the new rules for the quantization of angular momentum. As a byproduct, she showed that orbital angular momentum can only take integer values. Impressed by this contribution, Pauli invited her to collaborate on the susceptibility of gases. She then went to Tübingen, where many of the spectroscopic data were obtained that drove the transition from the old to the new quantum theory. It is hard to imagine better places to be in those years for young quantum physicists trying to make a name for themselves. This chapter describes these promising early stages of Mensing’s career and asks why she gave it up three years in. We argue that it was not getting married and having children that forced Lucy Mensing, now Lucy Schütz, out of physics, but the other way around. Frustration about her own research in Tübingen and about the prevailing male-dominated climate in physics led her to choose family over career.

Over the past hundred years or so, physicists have developed a foolproof and powerful tool that allows us to understand everything and anything in the universe. You take the object that you’re interested in and you throw something at it. Ideally, you throw something at it really hard. This technique was developed around the turn of the 20th century and has since allowed us to understand everything from the structure of atoms, to the structure of materials, to the structure of DNA. In short, throwing stuff at other stuff is the single most important experi- mental method available to science. Because of this, it is given a respectable sounding name. We call it scattering.