Maxwell's demon and the history of the second law of thermodynamics

I recently reread Warmth Disperses and Time Passes: The History of Heat by Hans Christian von Baeyer

As a popular book, it provides a beautiful and enthralling account of the discovery of the first and second laws of thermodynamics. The book is a great companion to teaching and learning thermodynamics and statistical mechanics. The narrative is unified by the puzzle of Maxwell's demon.

Aside: The book was first published in 1998 with the title Maxwell's Demon. My guess is that the publisher changed the title because most people have probably not heard of the demon, unlike Schrodinger's cat.

Baeyer captures both the wonder of the subject and the fascinating story of how the science of thermodynamics developed. He describes quirky personalities and illustrates how science proceeds with a mixture of brilliant insights, clever experiments, false leads, and forgotten discoveries. It is easy and compelling reading.

I appreciated that there is a lack of hype, in contrast to too many popular science books.

The book is enhanced by showing that the story is not over. Many reports of the demise of the demon have been premature. The penultimate chapter discusses Zurek's definition of entropy in terms of algorithmic randomness. The last chapter considers molecular motors, such as kinesin, which can be viewed as ratchets driven by thermal noise.

Physical insights

The first and second laws tell us something about the fundamental nature of the universe. Although they are macroscopic and may have some (debatable) microscopic justification,  they can be viewed as fundamental.

Central to the development of the first law was the notion of the mechanical equivalent of heat.

There are three rather different ways to formulate the second law: a Carnot cycle represents an engine of optimal efficiency, heat never passes from a cold to a hot body, and the arrow of time. It is profound that these formulations are equivalent and not something that was anticipated. We should marvel at this.

Entropy can be viewed as the absence of information. Consequently, the second law can be viewed as statistical.

Things I want to understand

A good book stimulates us to want to engage more with its subject. Some things I want to understand are the entropy of the initial state of the universe, Boltzmann's H theorem, Feynman's ratchet, Shannon's information theory, molecular motors, Zurek's definition of entropy, and Gerald Holton's book, Thematic origins of scientific thought.

A recent tutorial is A Friendly Guide to Exorcising Maxwell’s Demon, by A. de Oliveira Junior, Jonatan Bohr Brask, and Rafael Chaves

Beautiful things missed

As a popular book, I think the length and scope of topics are right. Nevertheless, in a longer book, here are some things I would enjoy reading about: the zeroth and third laws, the contributions of Gibbs, the ergodic hypothesis, Brownian motion and evidence for atoms, the role of thermodynamics (and statistical mechanics) in the development of quantum theory (blackbody radiation, Einstein solid, identical particle statistics, and the Sackur-Tetrode equation) and perhaps phase transitions.

Two quibbles

von Baeyer has a somewhat reductionist perspective that the true nature of thermodynamics was revealed by the microscopic descriptions of Maxwell and Boltzmann.

I will write separate posts on why I am not comfortable with the following two statements.

Temperature IS the average kinetic energy of molecules.

Entropy was mysterious until Boltzmann's definition S=k ln W. 

My best blog posts of 2025?

 Best wishes for the New Year!

Here is a list of the posts that I wrote last year that I hope get the most interest.

My review article on emergence. I wrote posts about emergence in a range of systems: thermodynamics, quantum gravity, economics,... They were drafts of sections for my review article. It may be best to just read the article.

Why is the state of universities such an emotional issue for me?

Undergraduates need to learn about the Ising model

I wrote a series of posts on so-called "spin-crossover" compounds. Here are two: Spin crossover is a misnomer, and Elastic interactions and complex patterns in binary systems

2025 Nobel Prize in Physics: Macroscopic quantum effects

As always, I welcome comments, feedback, and suggestions for new posts.

Hikes around Brisbane I recommend

My colleague, Carla Verdi, suggested I write this post. Here are a few short hikes that I enjoy. I list them in order of distance from Brisbane.

If you use the AllTrails app, you can find more details on my profile. I also recommend the book, Take a Walk in South East Queensland.

Tarcoola Track 

This is a path that follows the Brisbane River. It starts only a few minutes drive (or ten minutes walk) south of the UQ St Lucia campus. The best bit of the trail is the first few minutes, which is almost a rainforest. I do part of this trail several times a week as it is accessible from my house and nicely combines with a walk on the neighbouring public golf course.

More than one hundred bird species have been recorded along the track. I believe this list was started by Hugh Possingham.

Mount Coot-tha

This is about fifteen fifteen-minute drive from St. Lucia. You can also get a public bus there. The summit has a nice cafe with an amazing view of the city.

I do a two-hour hike there each week with my dog, Priya. There are many trails and different starting points to select from. It is amazing that you can be so close to the city and almost feel like you are in the wilderness, particularly when you get off the large and popular trails. One of the many joys of living in Brisbane.

In the summer, due to the heat, I often start walking not long after sunrise. I avoid tracks that are shared with mountain bikes. 

Favourite walks include passing by Simpson's Falls and JC Slaughter Falls. Here is an example. There is some amazing indigenous art near the Slaughter Falls.

White Rock - Spring Mountain Conservation Estate

This is on the southern edge of Brisbane, next to Springfield. It is about a 30 minute drive, outside of rush hour.

I recently did the Spring Mountain Loop via Mountain Creek Trail.

The hikes below involve a day trip because of the driving. I don't like driving and so only do them when I am in the area for another reason or staying overnight.

Glasshouse mountains

In good traffic, they are about a 90-minute drive north of Brisbane.

I recently completed the Mount Tibberoowuccum and Trachyte Circuit Loop

Springbrook National Park

A bit less than 2 hours' drive, provided that the highway to the Gold Coast is not busy.

Warrie Circuit is a classic.

Lamington National Park

There are many hikes starting at Binna Burra or O'Reilly's.

I recently completed the Daves Creek circuit. Amazing, except for the leeches.

What does learning to ride a bicycle teach us?

How do you learn to ride a bicycle? How do you teach someone to ride a bicycle? It is not easy to put this into words and that is an important point in itself. It may help to have some knowledge of the parts of the bicycle and their respective functions. It may help to know something about relevant physics such as inertia, the centre of gravity, and balance. It may help to have some practical advice about seat height, posture, the appropriate speed at which to pedal, and where to look when riding. 

Nevertheless, all that information may not help much. Some young children learn to ride without knowing any of this. They just watch other children doing it, get on bike, try it, and learn by trial and error. The more passionate they are about learning the more likely they may be to succeed.

The mind and body of a bicyclist focus on just a few things: looking where they are going, pedalling, steering, and a sense of balance. This information is integrated together, and the rider adjusts their direction, pedalling, and posture. Furthermore, that process of integration and adjustment involves much that is not the rider’s focus, and they may not even be directly aware of. A person’s sense of body awareness and coordination is shaped by biology, physique, experience, and training.

This example of bike riding illustrates several important things.  First, we can have the ability to do something without necessarily being able to articulate how we do it. Second, knowing requires personal commitment. It involves trust and risk. If a person is unwilling to trust or take risks, they may miss out on something good, such as the joy of riding a bicycle. Third, knowing requires integration of multifaceted information. Fourth, knowledge and understanding come from integrating our focus into an implicit background we may not even be aware of.

The example of riding a bike is valuable for understanding how we know (epistemology) because it is simpler and less fraught and emotionally charged than how we come to an understanding and make decisions about history, ethics, politics, religion, and the meaning of scientific knowledge. 

These observations draw on Michael Polanyi, including his book, The Tacit Dimension, published in 1966, but based on lectures he gave at Yale in 1962. He referred to the first point as tacit knowing, and the fourth point as the subsidiary-focal interaction. The relationship of the subsidiary and the focus is like the whole and the parts. Polanyi considered the idea of tacit knowledge his most important discovery.

Aside: Chapter 2 of The Tacit Dimension is entitled "Emergence" and discusses ideas similar to those that Phil Anderson promoted in 1972 in More is Different, without using the word "emergence." According to Google Scholar, The Tacit Dimension has been cited 45,000 times.

Elastic interactions and complex patterns in binary systems

One of the many beauties of condensed matter physics is that it can reveal and illuminate how two systems or phenomena that at first appear to be quite different actually involve similar physics. This is an example of universality: for emergent phenomena, many details don't really matter. One example is the similarities between superconductivity and superfluidity. A consequence of universality is that the same concepts, techniques, toy models, and effective theories can be used to describe a wide range of systems.

The complex organometallic molecules, known by the misnomer "spin crossover" compounds, exhibit a rich range of phase transitions and types of spatial order. Key aspects of the physics are the following.

• Each transition metal ion can be in one of two possible states: low-spin or high-spin. 
• The size of each molecular complex depends on the spin state.
• Consequently, the molecules interact with their neighbours via elastic interactions.

A toy model that can describe this is expanding balls connected by springs. Various versions of this type of model are reviewed here. The simplest version is the chain model below.

It turns out there are other classes of systems described by similar models. As far as I am aware, this was first pointed out in Consequences of Lattice Mismatch for Phase Equilibrium in Heterostructured Solids Layne B. Frechette, Christoph Dellago, Phillip L. Geissler

That paper is motivated by experiments on the growth of semiconductor quantum dots, by ion exchange, such as when CdSe is bathed in an Ag-rich solution and Ag2Se is produced with heterostructures (i.e., patterns of Ag and Se ions) that are different from the bulk crystal.

They consider the balls and springs model above on a triangular lattice.

They also point out how similar physics is relevant to binary metal alloys, e.g, AgCu, citing 

Ising model for phase separation in alloys with anisotropic elastic interaction—I. Theory, P. Fratzl and O. Penrose

Those authors consider a square lattice with elastic interactions associated with bond stretching along the edges and diagonals of the squares and bending of the square angles.

Frechette et al. also mention experiments on thin films of  DNA modified metallic nanoparticles. Compared to atomic systems these can tolerate larger lattice-mismatch before the formation of defects due to lattice strain.

Other systems (not mentioned) described by similar Ising models are metal-hydrogen systems, where the Ising pseudospin signifies whether a hydrogen atom is present at a particular site in the metallic crystal.

Frechette et al. start with the ball and springs model and "integrate out" the springs to obtain an effective Hamiltonian, which is an Ising model.

The spatial range of the interaction between Ising spins is shown in the colour-shaded plot below.

The interaction has two components.

One is an infinite range "ferromagnetic" part, seen as the light blue below.

The second is a short-range interaction which is mostly "antiferromagnetic" (i.e., red), but extends over several lattice sites. (Note, this interaction will be frustrated on the triangular lattice).

Using this toy model, Frechette et al. can obtain complex patterns (heterostructures) similar to those seen in quantum dots grown by ion exchange.

There is some subtle (and confusing) physics associated with deriving the Ising model from the ball and springs model. 

Due to the long-range nature of elastic interactions, the boundary conditions matter. 

The infinite range part of the Ising interaction arises from dealing with the lattice constant for the crystal, depending on the net "magnetisation" of the "spins". But that is a story for another day.

Why is the state of universities such an emotional issue for me?

It all about values!

Universities have changed dramatically over the course of my lifetime. Australian universities are receiving increasing media attention due to failures in management and governance. But there is a lot more to the story, particularly at the grassroots level, of the everyday experience of students and faculty. It is all about the four M's: management, marketing, metrics, and money. Learning, understanding, and discovering things for their own sake is alien and marginalised. I have stopped writing posts about this. So why come back to it?

I am often struck how emotional this issue is for me and how hard it is to sometimes talk about it, particularly with those with a different view from me. Writing blog posts (e.g. this one) about it has been a somewhat constructive outlet, rather than exploding in anger at an overpaid and unqualified "manager" or one of their many multiplying minions.

A few weeks ago, I listened to three public lectures by the Australian historian Peter Harrison. [He is my former UQ colleague. We are now both Emeritus. I benefited from excellent seminars he ran at UQ, some of which I blogged about].

The lectures helped me understand what has happened to universities and also why it is a sensitive subject for me. Briefly, it is all about values and virtues.

The lectures are nicely summarised by Peter in the short article, 

How our universities became disenchanted: Secularisation, bureaucracy and the erosion of value

Reading the article rather than this blog post is recommended. I won't try and summarise it, but rather highlight a few points and then make some peripheral commentary.

I agree with Peter's descriptions of the problems we see on the surface (bureaucracy, metrics, and management features significantly). His lectures are a much deeper analysis of underlying cultural changes and shifting worldviews that have occurred over centuries, leading universities to evolve into their current mangled form.

A few things to clarify to avoid potential misunderstanding of Peter's arguments.

Secularisation is defined broadly. It does not just refer to the decline in the public influence of Christianity in the Western world. It is also about Greek philosophy, particularly Aristotle, and the associated emphasis on virtues and transcendence. Peter states:

"The intrinsic motivations of teachers, researchers and scholars can be understood in terms of virtues or duties. According to virtue ethics, the “good” of an activity is related to the way it leads to a cultivation and expression of particular virtues. These, in turn, are related to a particular conception of natural human ends or goals. (Aristotle’s understanding of human nature, which informs virtue ethics, proposes that human beings are naturally oriented towards knowledge, and that they are fulfilled as persons to the extent that they pursue those goals and develop the requisite intellectual virtues.)"

The virtue ethics of Aristotle [and Alisdair MacIntyre] conflicts with competing ethical visions, including duty-oriented (deontological) ethics, consequentialist ethics, and particularly utilitarianism. This led to a shift away from intrinsic goods to what things are "good for", i.e., what practical outcomes they produce. For example, is scientific research "good" and have "value" because it cultivates curiousity, awe, and wonder, or because it will lead to technology that will stimulate economic growth?

Peter draws significantly on Max Weber's ideas about secularisation, institutions, and authority. Weber argued that a natural consequence of secularisation was disenchantment (the loss of magic in the world). This is not simply "people believe in science rather than magic". Disenchantment is a loss of a sense of awe, wonder, and mystery.

Now, a few peripheral responses to the lectures.

Is secularisation the dominant force that has created these problems for universities? In question time, Peter was asked whether capitalism was more important. i.e., universities are treated as businesses and students as customers? He agreed that capitalism is a factor but also pointed out how Weber emphasised that capitalism was connected to the secularising effects of the Protestant Reformation.

 I think that two other factors to consider are egalitarianism and opportunism. These flow from universities being "victims" of their own success. Similar issues may also be relevant to private schools, hospitals, and charities. They have often been founded by people of "charisma" [in the sense used by Weber] motivated by virtue ethics. Founders were not concerned with power, status, or money. What they were doing had intrinsic value to them and was "virtuous". In the early stages, these institutions attracted people with similar ideals. The associated energy, creativity, and common vision led to "success." Students learnt things, patients got healed, and poverty was alleviated. But, this success attracted attention and  the institution then had power, money, status, and influence.

The opportunists then move in. They are attracted to the potential to share in the power, money, status, and influence. The institution then takes on a life of its own, and the ideals and virtue ethics of the founders are squeezed out. In some sense, opportunism might be argued to be a consequence of secularisation. 

[Aside: two old posts considered a similar evolution, motivated by a classic article about the development of businesses.]

One indicator of the "success" of universities is how their graduates join the elite and hold significant influence in society. [Aside: ignoring the problem of distinguishing correlation and causality. Do universities actually train students well or just select those who will succeed anyway?]  Before (around) 1960, (mostly) only the children of the elite got to attend university. Demands arose that more people should have access to this privilege. This led to "massification" and an explosion in the number of students, courses, and institutions. This continues today, globally. Associated with this was more bureaucracy. Furthermore, the "iron triangle" of cost, access, and quality presents a challenge for this egalitarianism. If access increases, so does cost and quality decreases, unless you spend even more. It is wonderful that universities have become more diverse and accessible. On the other hand, I fear that for every underprivileged student admitted whose mind is expanded and life enriched, many more rich, lazy, and entitled students suck the life out of the system.

Metrics are pseudo-rational

Peter rightly discussed how the proliferation of the use of metrics to measure value is problematic, and reflects the "rationalisation" associated with bureaucracy (described by Weber). Even if one embraces the idea that "rational" and "objective" assessment is desirable, my observation is that in practice, metrics are invariably used in an irrational way. For example, managers look at the impact factor of journals, but are blissfully oblivious to the fact that the citation distribution for any journal is so broad and with a long tail that the mean number is meaningless. The underlying problem is that too many of the people doing assessments suffer from some mixture of busyness, intellectual laziness, and arrogance. Too many managers are power hungry and want to make the decisions themselves, and don't trust faculty who actually may understand the intellectual merits and weaknesses of the work being assessed.

The problems are just as great for the sciences as the humanities

On the surface, the humanities are doing worse than the sciences. For example, if you look at declining student numbers, threats of job cuts, political criticism, and status within the university. This is because science is associated with technology which is associated with jobs and economic growth. However, if you look at pure science that is driven by curiousity, awe, and wonder, then one should be concerned. There is an aversion to attacking difficult and risky problems, particularly those that require long-term investment or have been around for a while. The emphasis is on low-lying fruit and the latest fashion. Almost all physics and chemistry research is framed in terms of potential applications, not fundamental understanding. Sometimes I feel some of my colleagues are doing engineering not physics. In a similar vein, biochemists frame research in terms of biomedical applications, not the beauty and wonders of how biological systems work. 

Are universities destined for bureaucratic self-destruction?

Provocatively, Peter considered the potential implications of the arguments of historian and anthropologist Joseph Tainter concerning the collapse of complex societies. On the technical side, this reminded me of a famous result in ecology by Robert May, that as the complexity of a system (the number of components and interactions) increases, it can become unstable.

I don't think universities as institutions will collapse. They are too integrated into the fabric of modern capitalism. What may collapse is the production of well-educated (in the Renaissance sense) graduates and research that is beautiful, original, and awe-inspiring. This leads naturally into the following question.

Is the age of great discoveries over?

Peter briefly raised this issue. On the one hand, we are victims of our own success. It is amazing how much we now know and understand. Hence, it is harder to discover truly new and amazing things. On the other hand, because of emergence we should expect surprises.

There is hope on the margins

Peter did not just lament the current situation but made some concrete suggestions for addressing the problems, even though we are trapped in Weber's "iron cage" of bureaucracy.

• Re-balancing the structures of authority
• Finding a place for values discourse in the universities
• Develop ways of resolving differences with a sense of the rationality of Alisdair MacIntyre in mind

On the first, I note the encouraging work of the ANU Governance Project.

Peter also encouraged people to work on the margins. I also think that this is where the most significant scholarship and stimulus for reform will happen. A nice example is the story that Malcolm Gladwell tells in a podcast episode, The Obscure Virus Club.

Overdoped cuprates are not Fermi liquids

They are anisotropic marginal Fermi liquids.

A commenter on my recent AI blog post mentioned the following preprint, with a very different point of view.

Superconductivity in overdoped cuprates can be understood from a BCS perspective!

B.J. Ramshaw, Steven A. Kivelson

The authors claim:

" a theoretical understanding of the "essential physics" is achievable in terms of a conventional Fermi-liquid treatment of the normal state...

...observed features of the overdoped materials that are inconsistent with this perspective can be attributed to the expected effects of the intrinsic disorder associated with most of the materials being solid state solutions"

On the latter point, they mention two papers that found the resistivity versus temperature can have a linear component. But there is much more.

The authors appear unaware of the experimental data and detailed theoretical analysis showing that the overdoped cuprates are anisotropic marginal Fermi liquids. 

Angle-dependent magnetoresistance measurements by Nigel Hussey's group, reported in 2006, were consistent with a Fermi surface anisotropy in the scattering rate.

Papers in 2011 and 2012 pushed the analysis further.

Consistent Description of the Metallic Phase of Overdoped Cuprate Superconductors as an Anisotropic Marginal Fermi Liquid, J. Kokalj and Ross H. McKenzie

Transport properties of the metallic state of overdoped cuprate superconductors from an anisotropic marginal Fermi liquid model, J. Kokalj, N. E. Hussey, and Ross H. McKenzie 

The self-energy is the sum of two terms with characteristic dependencies on temperature, frequency, location on the Fermi surface, and doping. The first term is isotropic over the Fermi surface, independent of doping, and has the frequency and temperature dependence characteristic of a Fermi liquid. 

The second term is anisotropic over the Fermi surface (vanishing at the same points as the superconducting energy gap), strongly varies with doping (scaling roughly with 𝑇𝑐, the superconducting transition temperature), and has the frequency and temperature dependence characteristic of a marginal Fermi liquid. 

The first paper showed that this self-energy can describe a range of experimental data including angle-dependent magnetoresistance and quasiparticle renormalizations determined from specific heat, quantum oscillations, and angle-resolved photoemission spectroscopy. 

The second paper, showed, without introducing new parameters and neglecting vertex corrections, that this model self-energy can give a quantitative description of the temperature and doping dependence of a range of reported transport properties of Tl2Ba2CuO6+𝛿 samples. These include the intralayer resistivity, the frequency-dependent optical conductivity, the intralayer magnetoresistance, and the Hall coefficient. The temperature dependence of the latter two are particularly sensitive to the anisotropy of the scattering rate and to the shape of the Fermi surface.

For a summary of all of this, see slides from a talk I gave at Stanford back in 2013.

I am curious whether the authors can explain the anisotropic part of the self-energy in terms of disorder in samples.