200 Years Rudolph Clausius

Steam engines marked the beginning of the industrial age, the fallout from which causes us so many headaches today. But industrialization also made possible in the first place our understanding of modern physics and of the concept of energy in particular. Rudolph Clausius, the University of Bonn’s second professor of physics from 1869-1888, decisively shaped human insight into the development of the material world with his mechanical theory of heat and the concept of "entropy" – giving us the decisive clue as to why time has a direction. To this day, his theories form the very foundation from which we exercise control over material phenomena and, by extension, the processes of the industrial world. His concepts extend into the modern world of information processing and many other areas of scientific knowledge and its applications. In this first lecture, we will introduce important findings on the "motive power of heat" (as Clausius spoke of it; today we call it thermodynamics) and use demonstration experiments to gain initial insights that we can then relate to our present-day environment.

Video of the lecture on the YouTube channel of the University of Bonn

Terms from thermodynamics such as heat, temperature and energy are familiar to everyone. Surprisingly it was only in the nineteenth century that Mayer, Joule and Helmholtz and others realized  the relation between mechanical energy and temperature. Further progress was achieved when Carnot noticed that these physical concepts are not sufficient to describe the processes that take place in a steam engine. Clausius finally realized that another mysterious, physically measurable quantity had to be at work in heat transfer. This quantity he named entropy. In physics, entropy plays a fundamental role. The competition between energy, which becomes minimal in an ordered system, and entropy, which reaches its maximum in a completely disordered system, is responsible, for example, for the melting of a solid body. It was left to Boltzmann and Gibbs to relate the motion of atoms to thermodynamic quantities and thus discover what entropy really is.

This understanding of how the microscopic atomic motion and thermodynamics are related eventually led to Planck's discovery of quantum mechanics.

In my lecture, I will attempt to develop an intuitive understanding of entropy, giving examples of the competition between entropy and energy leading to order and disorder.

When Rudolph Clausius burst onto the academic scene in the mid-19th century, the natural sciences distinguished between two forms of matter: for one, the ponderable forms, i.e. all those substances that can be weighed, and, for another, the non-ponderable forms, which also included heat. At the time, common terms such as atom and molecule were not yet clearly defined and were still debatable in both physics and chemistry. The so-called caloricum, the "heat substance", fascinated Clausius in particular. As a pioneer of his time, Clausius unwaveringly applied the already familiar concepts from the mechanics of macroscopic bodies to a microscopic world composed of atoms and molecules. These reflections finally led him to the final break with the caloricum concept, and with that posit the foundation for a new mechanical theory of heat, i.e., thermodynamics. Eventually, this gave the sciences far-reaching insights expressed in terms like entropy and absolute (i.e., substance-independent) thermodynamic temperature. On the way to this groundbreaking theory, Clausius formulated relationships between energy, heat and temperature that are still valid today, not to mention fundamental principles of atomic and molecular motion in the three states of matter known to us as gas, liquid and solid. It would take more than a century after the publication of Rudolf Clausius' seminal writings before scientists at the boundary between physics and chemistry finally succeeded in visualizing the unimaginably fast motions of the building blocks of matter and their fundamental interactions at the molecular level.

Video of the lecture on the YouTube channel of the University of Bonn

On the thermodynamics of the atmosphere in the climate system: R. Clausius and the phase transitions of water

The importance of Rudolph Clausius to climate physics emerges clearly when one looks through the just- published Sixth Assessment Report of Working Group I (WG-I AR6, Climate Change 2021 The Physical Basis)1 of the Intergovernmental Panel on Climatic Change IPCC: Alone in Chapter 8 on the variability of the hydrological cycle in the climate system, the name "Clausius" comes up 12 times. This part of report deals in particular with the importance of the phase transitions of water between solid/liquid and gas for both the concentration variations of water vapor in the atmosphere as a greenhouse gas and the climatic variations of precipitation/rain. Of vital importance to these phase transitions is the Clausius-Clapeyron equation. In my contribution to the lecture series, I will summarize and illustrate the connections ranging from thermodynamic principles to applications in meteorology and climate dynamics.

Video of the lecture on the YouTube channel of the University of Bonn

The influence of Clausius' work on our knowledge of dark matter, black holes, gravity, and the expansion of the universe.

Almost 90 years ago, scientists found the first reliable evidence for the existence of dark matter. The basis for this was and is the "virial theorem" developed by Clausius as applied to the motion of galaxies in galaxy clusters. In the first part of the lecture we will illustrate this. In the second part (in English), we provide a basic introduction to the long-standing problem of the "entropy of the universe" and the contribution of black holes. This then prompts us to speculate on possible implications for the nature of gravity or the expansion of the universe.

Quantum chemical calculation of molecular entropy Entropy is a key property of matter which can be described by statistical thermodynamics. This requires knowledge of the discrete energy states of substances that are occupied at a given temperature, i.e., in the simplest case that of a single molecule. The lecture covers how these states can be calculated using modern methods of theoretical chemistry and which chemical properties of practical importance can be predicted in this way.

Video of the lecture on the YouTube channel of the University of Bonn

Further information will be provided soon.

Video of the lecture on the YouTube channel of the University of Bonn

For a long time, both heat equation and entropy have played a significant role in many areas of mathematics. In this talk, two features will be pointed out that were discovered only in the 21st century. On the one hand, the former Bonn colleague Felix Otto succeeded in showing that the heat equation can be obtained as a gradient flow of the entropy in the space of probability measures if we equip this space with the Kantorovich-Wasserstein metric from the theory of optimal mass transportation. On the other hand, the decades-long open question of a synthetic characterization of Ricci curvature bounds on manifolds or on more general "singular" space found its comprehensive answer in convexity properties of the entropy.

Clausius and theoretical chemistry: quantum cluster equilibrium

When molecules have many conformers of the same size and we are interested in how much a conformation contributes to a certain property, we usually address this using Boltzmann weights. However, if we want to include several oligomers of assorted sizes, for example a single-molecule monomer and dimer, we use what is called a cluster weighting. Similar to Boltzmann weighting, it involves combining simple models of statistical thermodynamics with quantum chemical calculations. The inclusion of different oligomers allows us to model the liquid as well as the gaseous state. By choosing a suitable cluster set, it becomes possible to model dissolved substances in different concentrations. Self-consistent calculations then yield equilibrium populations for the various clusters. These, in turn, allow computing important thermodynamic values by weighting the cluster partition function. In this lecture, we want to take a look at combining the historical Clausius-Clapeyron equation on cluster weighting with modern electronic structure methods and thus handle phase transitions of complex systems.

On the 200th birthday of Rudolph Clausius

Rudolph Clausius figures among the 19th century's most important physicists, a contemporary and colleague of luminaries like Helmholtz, Kirchhoff, Kelvin, Tyndall, Joule and Maxwell. In 1850 it was Clausius who first formulated the 2nd Law of Thermodynamics; furthermore, he was instrumental in establishing the kinetic theory of gases which served as the basis for the later work of Boltzmann, Gibbs, Planck and many others. Today, however, he is known almost solely for his introduction in 1865 of entropy as a state property and the "Clausius-Clapeyron" equation (and eventually the "Clausius-Mossotti" relation.) We know little about his life – surprisingly, we must do without a biography – and many original sources from his private life are probably lost. In my lecture, I will present a picture of his life and work based on my over 30-years’ search for documents and secondary sources from the world Clausius inhabited and enriched.

Bonn University's Physics Show presents a short play to help commemorate the birthday of Rudolph Clausius on January 2, 1822. With several fun live experiments, it brings Rudolph Clausius and some of his colleagues to life in an entertaining way.

Video of the lecture on the YouTube channel of the University of Bonn