Elizabeth Monroe, married Boggs (1913−1996), trained as a mathematician at Bryn Mawr, as a mathematical chemist at Cambridge, and as a theoretical chemist at Cornell, before joining the Manhattan Project at the Explosives Research Laboratory. Although her contributions to the fields of computational quantum chemistry, statistical mechanics, and explosives had lasting legacies, her scientific career nevertheless ended with World War II. The birth of her son, who suffered from severe developmental disabilities, prevented her from ever rejoining the research workforce. She pivoted instead to a remarkable life of public advocacy for people with disability, building on her scientific training to move research and policy forward. This chapters retraces how Monroe Boggs went from an early quantum chemistry enthusiast to a key figure of the disability rights movement.

Stationary charges give rise to electric fields. Moving charges give rise to magnetic fields. In this chapter, we explore how this comes about, starting with currents in wires which give rise to a magnetic field wrapping the wire.

Nonequilibrium steady states arise if a system is driven in a time-independent way. This can be realized through contact with particle reservoirs at different (electro)chemical potential for enzymatic reactions and for transport through quantum dot structures. For molecular motors, an applied external force contributes to such an external driving. Formally, such systems are described by a master equation with time-independent transition rates that are constrained by the local detailed balance relation. Characteristic of such systems are persistent probability currents. This stationary state is unique and can be obtained either through a graph-theoretic method or as an eigenvector of the generator. These systems have a constant rate of entropy production. Moreover, this entropy production fulfills a detailed fluctuation theorem. The thermodynamic uncertainty relation provides a lower bound on entropy production in terms of the mean and dispersion of any current in the system. An important classification distinguishes unicyclic from multicyclic systems. In particular for the latter, the concept of cycles and their affinities are introduced and related to macroscopic or physical affinities driving an engine. In the linear response regime, Onsager coefficients are proven to obey a symmetry.

In this chapter, we rewrite the Maxwell equations yet again, this time in the language of actions and Lagrangians that we introduced in the first book in this series. This provides many new perspectives on electromagnetism. Among the pay-offs are a deeper understanding, via Noether’s theorem, of the energy and momentum carried by electromagnetism fields. This will also allow us to explore a number of deeper ideas, including superconductivity, the Higgs mechanism, and topological insulators.

This chapter starts with a discussion of simple univariate chemical reactions networks emphasizing the need to impose thermodynamically consistent reaction rates. For a linear reaction scheme, the stationary distribution is given analytically as a Poisson distribution. Nonlinear schemes can lead to bistability. For large systems, the stationary solution can be expressed by an effective potential. Two types of Fokker–Planck descriptions are shown to fail in certain regimes. In the thermodynamic limit, the dynamics can be described by a simple rate equation. Entropy production is discussed on the various levels of description. A simple two-dimensional scheme, the Brusselator, can lead to persistent oscillations. Heat and entropy production are identified for an individual reaction event of a general multivariate reaction scheme.

In this chapter, we explore the basics of fluid mechanics. We will think about how to describe fluids and look at the kinds of things they can do.

Unusually, and a little defensively, the title of this chapter highlights what we won’t talk about, rather than what we will. Fluids have a property known as viscosity. This is an internal friction force acting within the fluid as diferent layers rub together. It is crucially important in many applications. In spite of its importance, we will start our journey into the world of fluids by ignoring viscosity altogether. Such flows are called inviscid. This will allow us to build intuition for the equations of fluid mechanics without the complications that viscosity brings. Moreover, the flows that we find in this section will not be wasted work. As we will see later, they give a good approximation to viscous flows in certain regimes where the more general equations reduce to those studied here.

The universe we live in is both strange and interesting. This strangeness comes about because, at the most fundamental level, the universe is governed by the laws of quantum mechanics. This is the most spectacularly accurate and powerful theory ever devised, one that has given us insights into many aspects of the world, from the structure of matter to the meaning of information. This textbook provides a comprehensive account of all things quantum. It starts by introducing the wavefunction and its interpretation as an ephemeral wave of complex probability, before delving into the mathematical formalism of quantum mechanics and exploring its diverse applications, from atomic physics and scattering, to quantum computing. Designed to be accessible, this volume is suitable for both students and researchers, beginning with the basics before progressing to more advanced topics.

Take anything in the universe, put it in a box, and heat it up. Regardless of what you start with, the motion of the substance will be described by the equations of fluid mechanics. This remarkable universality is the reason why fluid mechanics is important.

The key equation of fluid mechanics is the Navier-Stokes equation. This textbook starts with the basics of fluid flows, building to the Navier-Stokes equation while explaining the physics behind the various terms and exploring the astonishingly rich landscape of solutions. The book then progresses to more advanced topics, including waves, fluid instabilities, and turbulence, before concluding by turning inwards and describing the atomic constituents of fluids. It introduces ideas of kinetic theory, including the Boltzmann equation, to explain why the collective motion of 1023 atoms is, under the right circumstances, always governed by the laws of fluid mechanics.

In this chapter, we present the microscopic (Langevin equation) and macroscopic (Fokker–Planck equation) descriptions of Brownian motion and confirm their consistency. Furthermore, we provide a detailed introduction to the Poisson process, which forms the foundation of chemical reactions. Subsequently, we introduce the chemical Langevin equation and its corresponding Fokker–Planck equation, which are utilized in modeling molecular number fluctuations in chemical reactions. We also explain stochastic differential equations with both the Ito and Stratonovich types of integrals. Exploring mechanisms arising from the presence of noise, we discuss noise-induced transitions and attractor selection and adaptation in dynamical systems, elucidating their functional significance in cells. Finally, as an advanced topic, we introduce adiabatic elimination in stochastic systems.

Rare or extreme fluctuations beyond the Gaussian regime are treated through large deviation theory for the nonequilibrium steady state of discrete systems and of systems with Langevin dynamics. For both classes, we first develop the spectral approach that yields the scaled cumulant-generating function for state observables and currents in terms of the largest eigenvalue of the tilted generator. Second, we introduce the rate function of level 2.5 that can be determined exactly. Contractions then lead to bounds on the rate function for state observables or currents. Specialized to equilibrium, explicit results are obtained. As a general result, the rate function for any current is shown to be bounded by a quadratic function which implies the thermodynamic uncertainty relation.