Maxwell’s Demon Meets Nonequilibrium Quantum Thermodynamics

 Following measurements of a spin system driven out of thermal equilibrium (red), Serra and colleagues’ Maxwell's demon (blue) implements feedback control on the system’s dynamical state [2]. The control is similar to that of a parachute, smoothening the transition of the system from one state to another and rectifying the associated entropy production.
Experimental rectification of entropy production by a Maxwell’s Demon in a quantum system
P. A. Camati, J. P. S. Peterson, T. B. Batalhão, K. Micadei, A. M. Souza, R. S. Sarthour, I. S. Oliveira, R. M. Serra

Maxwell’s demon explores the role of information in physical processes. Employing information about microscopic degrees of freedom, this “intelligent observer” is capable of compensating entropy production (or extracting work), apparently challenging the second law of thermodynamics. In a modern standpoint, it is regarded as a feedback control mechanism and the limits of thermodynamics are recast incorporating information-to-energy conversion. We derive a trade-off relation between information-theoretic quantities empowering the design of an efficient Maxwell’s demon in a quantum system. The demon is experimentally implemented as a spin-1/2 quantum memory that acquires information, and employs it to control the dynamics of another spin-1/2 system, through a natural interaction. Noise and imperfections in this protocol are investigated by the assessment of its effectiveness. This realization provides experimental evidence that the irreversibility on a non-equilibrium dynamics can be mitigated by assessing microscopic information and applying a feed-forward strategy at the quantum scale.

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Entropic Measure of Time, and Gas Expansion in Vacuum

Leonid M. Martyushev, Evgenii V. Shaiapin
The study considers advantages of the introduced measure of time based on the entropy change under irreversible processes (entropy production). Using the example of non-equilibrium expansion of an ideal gas in vacuum, such a measure is introduced with the help of Boltzmann’s classic entropy. It is shown that, in the general case, this measure of time proves to be nonlinearly related to the reference measure assumed uniform by convention. The connection between this result and the results of other authors investigating measure of time in some biological and cosmological problems is noted…

Maxwell’s demon as a self-contained, information-powered refrigerator

Scientists created a nano-scale device that may facilitate the design of future computers, for example.

An autonomous Maxwell's demon. When the demon sees the electron enter the island (1.), it traps the electron with a positive charge (2.). When the electron leaves the island (3.), the demon switches back a negative charge (4.). Image: Jonne Koski.

An autonomous Maxwell’s demon. When the demon sees the electron enter the island (1.), it traps the electron with a positive charge (2.). When the electron leaves the island (3.), the demon switches back a negative charge (4.). Image: Jonne Koski.

In 1867, Scottish physicist James Clerk Maxwell challenged the second law of thermodynamics according to which entropy in a closed system must always increase. In his thought experiment, Maxwell took a closed gas container, divided it into two parts with an inner wall and provided the wall with a small trap door. By opening and closing the door, the creature – ‘demon’ – controlling it could separate slow cold and fast warm particles to their respective sides, thus creating a temperature difference in contravention of the laws of thermodynamics.

On theoretical level, the thought experiment has been an object of consideration for nearly 150 years, but testing it experimentally has been impossible until the last few years. Making use of nanotechnology, scientists from Aalto University have now succeeded in constructing an autonomous Maxwell’s demon that makes it possible to analyse the microscopic changes in thermodynamics. The research results were recently published in Physical Review Letters. The work is part of the forthcoming PhD thesis of MSc Jonne Koski at Aalto University.

‘The system we constructed is a single-electron transistor that is formed by a small metallic island connected to two leads by tunnel junctions made of superconducting materials. The demon connected to the system is also a single-electron transistor that monitors the movement of electrons in the system. When an electron tunnels to the island, the demon traps it with a positive charge. Conversely, when an electron leaves the island, the demon repels it with a negative charge and forces it to move uphill contrary to its potential, which lowers the temperature of the system,’ explains Professor Jukka Pekola.

What makes the demon autonomous or self-contained is that it performs the measurement and feedback operation without outside help. Changes in temperature are indicative of correlation between the demon and the system, or, in simple terms, of how much the demon ‘knows’ about the system. According to Pekola, the research would not have been possible without the Low Temperature Laboratory conditions.

‘We work at extremely low temperatures, so the system is so well isolated that it is possible to register extremely small temperature changes,’ he says.

‘An electronic demon also enables a very large number of repetitions of the measurement and feedback operation in a very short time, whereas those who, elsewhere in the world, used molecules to construct their demons had to contend with not more than a few hundred repetitions.’

The work of the team led by Pekola remains, for the time being, basic research, but in the future, the results obtained may, among other things, pave the way towards reversible computing.

‘As we work with superconducting circuits, it is also possible for us to create qubits of quantum computers. Next, we would like to examine these same phenomena on the quantum level,’ Pekola reveals.

J. V. Koski, A. Kutvonen, I. M. Khaymovich, T. Ala-Nissilä and J. P. Pekola: On-chip Maxwell’s demon as an information-powered refrigerator.

The abstract of the article can be read at

Check also Sebastian Deffner’s Viewpoint: Exorcising Maxwell’s Demon at


See also, how Maxwell’s demon converts information to energy with the help of nanotechnology.


Energy Flows in Low-Entropy Complex Systems

cosmic evolutionEric J. Chaisson
Nature’s many complex systems–physical, biological, and cultural–are islands of low-entropy order within increasingly disordered seas of surrounding, high-entropy chaos. Energy is a principal facilitator of the rising complexity of all such systems in the expanding Universe, including galaxies, stars, planets, life, society, and machines. A large amount of empirical evidence–relating neither entropy nor information, rather energy–suggests that an underlying simplicity guides the emergence and growth of complexity among many known, highly varied systems in the 14-billion-year-old Universe, from big bang to humankind. Energy flows are as centrally important to life and society as they are to stars and galaxies. In particular, the quantity energy rate density–the rate of energy flow per unit mass–can be used to explicate in a consistent, uniform, and unifying way a huge collection of diverse complex systems observed throughout Nature. Operationally, those systems able to utilize optimal amounts of energy tend to survive and those that cannot are non-randomly eliminated.
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An Exploration of the Limits of the Maxwell-Boltzmann Distribution

The probability distribution of speeds is given in terms of the dimensionless variable x = v/vp, where vp is the most probable speed.

The probability distribution of speeds is given in terms of the dimensionless variable x = v/vp, where vp is the most probable speed.

Yi-Chi Yvette Wu, L. H. Ford
Selected aspects of the Maxwell-Boltzmann for molecular speeds are discussed, with special attention to physical effects of the low speed and high speed limits. We use simple approaches to study several topics which could be included in introductory courses, but are usually only discussed in more advanced or specialized courses…
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Physicists create SQUID-like Bose–Einstein condensate

Illustration of how the BEC torus is cut by a green laser. The laser is rotated about the axis of the torus such that the cut moves through the torus. (Courtesy: K C Wright et al. 2013 Phys. Rev. Lett.)

Illustration of how the BEC torus is cut by a green laser. The laser is rotated about the axis of the torus such that the cut moves through the torus.

K. C. Wright, R. B. Blakestad, C. J. Lobb‡, W. D. Phillips, and G. K. Campbell
We have observed well-defined phase slips between quantized persistent current states around a toroidal atomic (23Na) Bose-Einstein condensate. These phase slips are induced by a weak link (a localized region of reduced superfluid density) rotated slowly around the ring. This is analogous to the behavior of a superconducting loop with a weak link in the presence of an external magnetic field. When the weak link is rotated more rapidly, well-defined phase slips no longer occur, and vortices enter into the bulk of the condensate. A noteworthy feature of this system is the ability to dynamically vary the current-phase relation of the weak link, a feature which is difficult to implement in superconducting or superfluid helium circuits.
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Ultracold fermions simulate spin–orbit coupling

Artist’s impression of the spin diode created by researchers at MIT. Atoms with clockwise spin can only move in one direction, while atoms with anticlockwise spin move in the opposite direction. (Courtesy: Christine Daniloff)

Two independent groups of physicists are the first to use ultracold fermionic atoms to simulate “spin–orbit coupling” – an interaction that plays an important role in the electronic properties of solid materials. Both experiments were done by firing laser beams at the atoms, which caused their momentum to change by an amount that depends on their intrinsic spin. Because the interactions between atoms in such simulations can be adjusted with great precision, the breakthrough could shed further light on a range of physical phenomena, including magnetism, topological insulators and Majorana fermions.

Spin–orbit coupling describes the interaction between the intrinsic spin of an electron in a material and the magnetic field induced by the electron’s movement relative to its surrounding ions. As well as playing a key role in the magnetic properties of materials, spin–orbit coupling also influences the performance of “spintronic” devices – those that exploit the spin, rather than the charge, of electrons and that could one day lead to faster and more energy-efficient computers.

Quantum simulators

Because of its fundamental nature, physicists are therefore very keen to use clouds of ultracold atoms to simulate spin–orbit coupling. Such “quantum simulations” are carried out by subjecting the gas to laser light and magnetic fields, which lets researchers create interactions between atoms that are similar to those experienced by electrons in a solid. The advantage of these simulations is that – unlike in a solid – the strength of these interactions can be easily adjusted, allowing physicists to test theories of condensed-matter physics.

In 2011 Ian Spielman and colleagues at the National Institute of Standards and Technology (NIST) in Maryland were the first to simulate spin–orbit coupling in an ultracold gas of bosonic atoms. Now, two independent groups – one in China led by Hui Zhai of Tsinghua University and Jing Zhang of Shanxi University, and the other in the US headed by Martin Zwierlein and Lawrence Cheuk at the Massachusetts Institute of Technology (MIT) – have extended Spielman’s technique to fermions. As electrons are fermions and not bosons, the new work is much more relevant to electron physics.

Using potassium-40…

The Chinese team began with about two million potassium-40 atoms that are held in an optical trap and cooled to well below the ensemble’s Fermi temperature. This means that nearly all the atoms in the gas are in the lowest possible energy state, like the conduction electrons in a metal. The team focused on two closely spaced magnetic energy states, which are used to simulate the spin of the electron – one state corresponding to spin up and the other to spin down.

The team then fired two laser beams into the gas from opposing directions. The laser light is set to resonate with a transition between the two spin states – a process that involves the atoms continuously absorbing and emitting photons. As these photons carry momentum, if an atom absorbs a photon moving in one direction and then re-emits it in the same direction, the atom’s momentum will not change. However, an atom can also be stimulated by the opposing beam to emit the photon in the opposite direction – thus changing the atom’s momentum. Such an interaction involves a change in the direction of the atom’s spin and is therefore analogous to spin–orbit coupling – albeit in 1D.

The Chinese team used its system to study several aspects of spin–orbit coupling. In one experiment, the researchers began with a state in which all the spins are initially pointing in the same direction. They then turned on the spin–orbit interaction by pulsing the lasers for a very short time – just a few hundred microseconds. They found that the spins began to point in different directions in a process known as “dephasing”. This is expected from fermions because atoms with the same spin cannot have the same momentum and therefore each atom will be affected differently by the spin–orbit interaction.

Understanding dephasing is important because it has a detrimental effect on technological applications of spin such as spintronics and quantum computing. The team also looked at several other effects related to spin–orbit coupling, including its effect on the momentum distribution of the atoms.

…and lithium-6

The MIT physicists, meanwhile, used a gas of lithium-6 atoms, which meant that their realization of spin–orbit coupling was more difficult than for the Chinese team. The problem is that lighter atoms such as lithium are more prone to heating via the resonant absorption of light. So to get round this problem, the MIT team kept most of its atoms in “reservoir states” in which they do not interact with the light and stayed cool – using radio waves to drive a small number of atoms into the spin–orbit coupling states.

The MIT team focused on showing that ultracold atoms can be used to simulate a “spin diode” – a device that is likely to play a key role in the development of spintronic circuits. It allows spin-up atoms to flow forwards but not backwards, and spin-down atoms backwards but not forward. “The gas acts as a quantum diode, a device that regulates the flow of spin currents,” says Cheuk.

Simulating band structure

By applying radio-frequency radiation to the gas, the MIT physicists were also able to simulate a periodic potential similar to that found in a 1D lattice. As expected for real materials, the periodic potential led to the existence of spin-dependent energy bands. According to the team, the ability to create spin-dependent band structures in this way could lead to the simulation of topological insulators.

The spin–orbit coupling simulated by both teams occurs only in 1D and therefore cannot be used to simulate the 2D and 3D systems found in most real-life electronic devices. However, there are several interesting scenarios that can be investigated in a 1D system. For example, it could be used to simulate the behaviour of electrons in semiconductor/superconductor nanowires. Such systems are believed to harbour quasiparticles that resemble Majorana fermions – long sought-after particles that are also their own antiparticle.

Both experiments are described in Physical Review Letters.
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