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FQXI ARTICLE

December 2, 2020

Thermo-Demonics

A devilish new framework of thermodynamics, which focuses on how we observe information, could help illuminate our understanding of probability and rewrite quantum theory.

FQXi Awardees: Benjamin Schumacher, Michael Westmoreland

March 4, 2019

Michel Westmoreland & Benjamin Schumacher

The framework, which is being developed by physicist Benjamin Schumacher, at Kenyon College in Gambier, Ohio, and mathematician Michael Westmoreland, at Denison University in Granville, Ohio, was given this devilish moniker by their colleagues because it put information at the center—along with a hypothetical, microscopic observer known as Maxwell’s demon. With the help of an FQXi grant of over $70,000, Schumacher and Westmoreland hope it will also enable them to remove the confusion over measurement and uncertainty in quantum theory.

Schumacher and Westmoreland realised they were kindred spirits in the 1990s. Both were interested in how information theory could help illuminate quantum mechanics and began to collaborate. In the quantum realm, observers typically know very little about where a particle is, or how fast it is moving, or how it is spinning. They have to make a measurement to reduce that uncertainty. In information theory, likewise, the information you gain when you learn something about a system is mathematically defined to be the reduction in your uncertainty about it. If you have a single ASCII character, for example, but only know that it is alphanumeric, there are 62 possibilities: 26 lowercase letters + 26 uppercase letters + 10 digits. But once you learn that the character is, say, F, you reduce the uncertainty from 62 to 1, and gain a corresponding amount of information.

I started wondering

if information is

more fundamental

than probabilities.

if information is

more fundamental

than probabilities.

- Michael Westmoreland

Making sense of this measurement problem is the "most fundamental problem in all of quantum mechanics," says William Wootters, a physicist at Williams College in Williamstown, Massachusetts, and a pioneer of quantum information theory.

Schumacher and Westmoreland have taken on that challenge. By the mid-2000s, they were trying to codify their work and that of many others in an undergraduate textbook on quantum mechanics from an information point of view (

That question led the two researchers to start thinking harder about the physics of the observer. They formulated the notion of an ’eidostate’—"a description of the world that exists as a physical state, and in which changes involve physical processes," says Schumacher. (The name comes from the Greek word ’eidos’ meaning "to see.")

Maxwell’s Demon

By choosing when to open and close the door, the demon causes one chamber to warm

up and the other to cool.

Credit: Htkym, Wikicommons

Maxwell left this paradox to later generations of physicists as a kind of homework assignment: Where was the flaw in this thought experiment? What would keep Maxwell’s ’demon’, as other physicists took to calling it, from violating the second law? Did the demon’s ability to observe, think, and act change the fundamental physics in some way? Or was its ’intelligence’ still governed by natural law?

Information Erasure

The solution that’s most widely accepted was given in 1982 by IBM physicist Charles Bennett, who based it on work that the late IBM physicist Rolf Landauer published in 1960. Yes, Bennett argued, a demon could, in theory, create an apparent violation of the second law through a completely automated process that required no intelligence whatsoever—but only if it retained information about every interaction with every molecule it had ever encountered. Once it started erasing that information, as any finite automata would eventually have to do, it would release energy back into the environment at exactly the rate (prescribed by ’Landauer’s principle’) required to preserve the second law.

A lot of physicists took Landauer’s minimum energy limit as a challenge, and immediately started pointing out special situations where it could be violated, notes Bennett. To clarify the resulting confusion, Schumacher and Westmoreland reworked Landauer’s principle into an elegantly simple formulation of the second law that took all the exceptions into account:

Human or Demon?

A thermodynamic price is always paid when observers, of any form, process information

and act on it.

Credit: LPETTET, istock

Schumacher’s words "had a very salutary effect," recalls Bennett. He notes that Schumacher and Westmoreland, who are both at smaller schools that emphasize teaching, had simplified elements of thermodynamics—"just the way it should be in a textbook."

Since then, Schumacher and Westmoreland have expanded that insight. "What we find is that a few very simple axioms about information can serve as a foundation for thermodynamics," says Schumacher, "including some things we didn’t expect." For example, the axioms contain no notion of probability, but they were able to derive a notion of probability from them (A. Hulse, B. Schumacher & M. D. Westmoreland,

Quantum theory is next in their sights. Eidostates should be well suited to the task, says Westmoreland because "they’re built to accommodate indeterminacy."

They are as eager as anyone to see where that will lead. "Understanding quantum mechanics is no mean feat—we haven’t done it yet!" says Wootters. "It may be that in order to get there, we’ll have to completely reframe the theory." If that’s the case, he says, "this particular point of view that Ben and Mike are taking might help us see our way to whatever comes next."

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JOHN R. COX wrote on May 11, 2019

If you have gotten curious from the results of a spherical condensate and have played with a little reverse engineering (and aren't afraid of argumentation in pure mathematics) but ran into a problem getting duplicate results, it is likely that is because electronic calculators and calculation programs are engineered at the microprocessor level to NOT do certain functions. Everyone is familiar with entering X divided by zero and getting a display result that says 'error'. Same way with...

If you have gotten curious from the results of a spherical condensate and have played with a little reverse engineering (and aren't afraid of argumentation in pure mathematics) but ran into a problem getting duplicate results, it is likely that is because electronic calculators and calculation programs are engineered at the microprocessor level to NOT do certain functions. Everyone is familiar with entering X divided by zero and getting a display result that says 'error'. Same way with...

ANONYMOUS wrote on April 23, 2019

One final note; If you look at Coulomb's Law it is a derivative of inverse square law which as with SR is an invariance function. Invariably, 1/r^2 will obtain in measurement from A to B, OR (but not and) B to A. A & B are seperate inertially bound objects. But in a single inertially bound field, that relationship is covariant to the upper density bound, A & B are different magnitudes of density in the same field and vary by the inverse of exponential rate, (1/e). Ineractive fields in regions of...

One final note; If you look at Coulomb's Law it is a derivative of inverse square law which as with SR is an invariance function. Invariably, 1/r^2 will obtain in measurement from A to B, OR (but not and) B to A. A & B are seperate inertially bound objects. But in a single inertially bound field, that relationship is covariant to the upper density bound, A & B are different magnitudes of density in the same field and vary by the inverse of exponential rate, (1/e). Ineractive fields in regions of...

ANONYMOUS wrote on April 21, 2019

Again, thanks Steve, it is in your wheelhouse. So if you and others wish to play with it, the empirical values in computation were as follows:

c = 2.997925^10 cm/sec

h = 6.626196^-27 erg/sec^-1

Boltzmann = 1.380648^-16 erg/Kelvin*

e generated by algebraic OS of calculator; key ( 1, INV, lnx, =, store)

Water trickles towards towards a floor drain on a well laid concrete floor because the drain is about 3cm lower than at the sidewall 5m away. A bowling ball...

Again, thanks Steve, it is in your wheelhouse. So if you and others wish to play with it, the empirical values in computation were as follows:

c = 2.997925^10 cm/sec

h = 6.626196^-27 erg/sec^-1

Boltzmann = 1.380648^-16 erg/Kelvin*

e generated by algebraic OS of calculator; key ( 1, INV, lnx, =, store)

Water trickles towards towards a floor drain on a well laid concrete floor because the drain is about 3cm lower than at the sidewall 5m away. A bowling ball...

read all article comments