ENTROPY: A BAFFLING CONCEPTION?

Dick Pountain /The Political Quarterly/ 22 May 2025 02:06

Book Review: Entropy Economics: The Living Basis Of Value And Production by James K. Galbraith and Jing Chen; University Of Chicago Press 2025; pp248; £25.76

“The second law is the most metaphysical law of physics since it points out without interposing symbols, without artificial devices of measurements, the direction in which the world is going.”
— Henri Bergson, Creative Evolution (1907)

Thermodynamics is possibly the branch of science that’s least understood, and least enjoyed, by the general public. People who didn’t take A-level Physics will probably only be familiar with a couple of its concepts, namely ‘entropy’, understood as a synonym for chaos, and ‘the Second Law’ as a portent of doom, the eventual demise of everything including the universe itself. Neither understanding is entirely wrong, but neither is especially useful. In fact thermodynamics is the most profound way of understanding the world and everything we undertake in it, mostly because of the constraints it imposes which may well explain its unpopularity). It’s why we can’t have perpetual motion machines, why climate change happens and is so hard to mitigate, and why we age. 

The internet is full of clever visualisations that explain difficult science topics, but the most popular by far are about quantum mechanics and cosmology, not thermodynamics. The weird incomprehensibility of quantum behaviour can be misinterpreted as making room for magic, the glorious star-scapes from the James Wigg Telescope show us the vastness of space (which Elon Musk and Jeff Bezos would like to open up as a holiday destination). Thermodynamics merely explains frostily why it ain’t going to happen…

In fact entropy is neither chaos nor order but rather a universally applicable concept that distinguishes between them – it’s a quantitative property that can be measured, but explaining it in plain language is hard. (Albert Mathews’ 1927 work ‘The Nature of Matter, Gravitation, and Light’ labelled it “an extremely baffling conception”). The idea arose historically from studying the physics of steam engines and observing that heat will only spontaneously flow from hot places to cooler places, never in the opposite direction. Such a heat flow can be harnessed to perform work, which increases the overall entropy of the system. Reversing the flow (say in a refrigerator) requires exerting work. 

Physicists soon realised that entropy applies not just to heat but to all forces of nature that evolve in the direction of less orderliness, the basis of the infamous Second Law. In particular it applies to all living things and hence to humans – we all age, die and decompose thus increasing the entropy of the universe.
Humans have understood from ancient times that the Sun is what gives us light, life and sustenance. Nowadays we know that plants employ chlorophyll to trap sunlight and turn carbon dioxide from the air into sugars, which animals eat to make proteins from which to make their mobile bodies. The Earth actually re-radiates all the energy it receives from sunlight back into space, but at a lower quality than it received. That quality consumed is entropy, and it drives all living things, ocean circulation, the weather…

James K. Galbraith and Jing Chen believe that entropy also applies to human institutions like the economy. Galbraith (son of J.K.Galbraith, famous 1960s exponent of Keynesian economics) is Professor of Government-Business Relations at the University of Texas, specialising in inequality studies; Jing is a Professor of Mathematics at the University of British Columbia and specialises in the physical basis of economics. Their book is a collaborative critique of mainstream economic theory, which they regard as a mathematical travesty unable to fully model problems of the real world.

They claim that the standard equilibrium model of the economy, which matches supply with demand, is an ideological construct that portrays capitalism as politically neutral, inevitable and eternal (in rather the same way that Fukuyama’s ‘End Of History’ represented geopolitics). Equilibrium theory treats recessions and crashes as unfortunate deviations from the perfect self-regulation of markets, and also fails to deal realistically with resources, which it regards as infinitely available, and with waste products which it tries to hide because they’re not profitable.

Galbraith and Jing set out an alternative theory that’s biophysically realistic to oppose this quasi-religious belief in self-regulating and all-knowing markets:

“The theories of value and production are the foundations of economic theory. Both should be consistent with life processes and physical laws […] Given the universality of the entropy law, it is natural to suspect that entropy somehow forms the basis of economic value. And indeed, this thought is not entirely new; an entropy theory of value is a scarcity theory, very familiar in the history of economic thought”

 To build this biophysically realistic theory the authors adopt an insight from Claude Shannon – the American electrical engineer father of Information Theory – that entropy and information are connected by a logarithmic relationship. We all recognise what exponential growth looks like: the reproduction of rabbits or locusts, the burning of gunpowder, any process that grows bigger and bigger, faster and faster. A logarithmic process is more or less the opposite, one that starts fast and then slows down: it’s a template for modelling decline and exhaustion, like diminishing returns, depreciation of machinery, decay, decomposition and ageing. In short, 2nd Law Entropy. Galbraith and Jing take Shannon’s formula and turn it into their definition of economic value:

V is value, P is the probability, that is the scarcity, of some resource or artefact, and b is its number of suppliers. (Don’t panic, this is the only formula I intend to present here). Their first two chapters examine equilibrium and non-equilibrium dynamics, linear, non-linear and chaotic systems, boundaries and inequalities, the role of regulation and government, to analyse the shortcomings of equilibrium economics and justify the need for biophysical realism.

Chapter 3 examines previous theories of value: the Labour theories of Ricardo, Marx, Sraffa and Pasinetti; the Utility theories of Jevons, Marshall and Arrow-Debreu, and the Scarcity theories of Walras, Schumpeter and Georgescu-Roegen. Chapters 4, 5 and 6 unfold their own entropy/scarcity based theories of value, resource use and production, and apply these to some simple examples. In the economic sphere production means taking low-entropy resources – say a seam of metal ore or coal in the ground – then mining, burning, smelting, forging, manufacturing and widely distributing the products, so increasing their value. Value may also be increased by by other means:

“In practice, the most important method to enhance valuation is to reduce the number of providers, creating monopoly or oligopoly. Governments enjoy many forms of monopoly, including over legalized violence, judicial punishments, and taxation. Governments grant monopolies, through patents, intellectual property rights, regulation, and industry standards. Businesses seek monopoly through technological innovation and market dominance, sometimes legal and sometimes not. Unions seek monopolies in bargaining — also called countervailing power— to help workers enjoy some of the fruits of their employers’ monopoly power.”

 Chapter 7 expounds Chen’s full mathematical treatment of their theory of production. I’m fairly adept at differential calculus but this goes way, way beyond my pay-grade (it involves partial differential equations and Richard Feynman’s path integrals for stochastic processes). We know that during the derivatives boom that preceded the 2007-8 Wall Street crash, brokers were recruiting young particle physicists straight out of MIT and Caltech, because pricing complex future derivatives demands their level of mathematical skill. They came up with the infamous Black-Scholes Equation, which worked very well until it didn’t… 

Chen’s production equation turns out to be effectively the same thing with a minus sign in front of it, which changes it from being about finance (how much to pay for risky stock-market speculations today) to production (what future returns to expect from capital investment today).

The final chapter 8, ‘Life in a World without Equilibrium’, collects together the implications of the authors’ new theories for the future of energy usage, climate change and demography, a disturbing conclusion that departs some way from mainstream progressive opinion. Readers of this journal who aren’t professional economists may find this chapter alone justifies reading the book.

Mainstream economists assume constant returns to scale, so that ever-increasing resource use will yield ever-increasing outputs, but in the real world finite resources can be depleted – and that applies to human labour, water, soil, even land. The unique chemical properties of carbon permitted the emergence of all our life forms: all the major non-renewable energy sources we depend upon – coal, oil, natural gas – arose from the fossilised remains of living carbon-based organisms. Our civilisation is the Fossil Fuel Civilisation, but it’s increasing the cost of all these low-entropy, high-quality resources while causing warming of the climate, rising of sea levels and a decline of human fertility. Avoiding these pitfalls will require us to move away from burning fossil fuels to alternative renewable energy sources – some existing, others still being developed – and to do that we have to accurately determine their Energy Return on Investment (EROI), which encompasses all the actual costs of research and deployment. Only if EROI is greater than one does that technology provide net energy to society. 

However monetary returns – especially in economies with large degrees of monopoly – don’t always provide an accurate measure of EROI, thanks to intervention by powerful interest groups (the sums involved are enormous). The authors consider two prominent kinds of renewable energy, corn-based ethanol and photovoltaic solar power, and conclude that low EROI makes these only viable with government subsidy:

“It is difficult to rule out the possibility that human beings can develop new technologies that have significantly higher overall efficiency in energy use than other living organisms and our own ancestors. But if research and development costs are included, the likelihood will be low. Human beings, like other dominant species, excel at extracting resources, not at using resources more efficiently.”

 They conclude that we will most likely fail to deal with global heating, that a warmer climate with raised levels of CO₂ will probably ‘green’ the Earth by enhancing plant growth, but not nearly fast enough to prevent the collapse of our current economic structures. Much of our current infrastructure will be rendered obsolete and economic activity unprofitable:

“The future of human society is likely, for a long time, to devolve back to smaller populations, shorter life spans, higher variable costs, and lower fixed costs, along with smaller countries and harsher inequalities both within and between them. Social arrangements, advance planning, new energy sources, and new investments can mitigate the suffering from this transition, up to a point. But this, very likely so far as we understand it, is the biophysical reality with which future economists, engineers, and planners will have to engage.”

Enjoy the rest of your day.