What is the Entropy in Entropic Gravity?

Sean M. Carroll, Grant N. Remmen
Abstract
We investigate theories in which gravity arises as an entropic force. We distinguish between two approaches to this idea: holographic gravity, in which Einstein’s equation arises from keeping entropy stationary in equilibrium under variations of the geometry and quantum state of a small region, and thermodynamic gravity, in which Einstein’s equation emerges as a local equation of state from constraints on the area of a dynamical lightsheet in a fixed spacetime background.
Examining holographic gravity, we argue that its underlying assumptions can be justified in part using recent results on the form of the modular energy in quantum field theory. For thermodynamic gravity, on the other hand, we find that it is difficult to formulate a self-consistent definition of the entropy, which represents an obstacle for this approach. This investigation points the way forward in understanding the connections between gravity and entanglement (…)

Conclusions
The idea that gravity can be thought of as an entropic force is an attractive one. In this paper we have distinguished between two different ways of implementing this idea: holographic gravity, which derives the Einstein equation from constraints on the boundary entanglement after varying over different states in the theory, and thermodynamic gravity, which relates the time evolution of a cross-sectional area to the entropy passing through a null surface in a specified spacetime.
We argued that holographic gravity is a consistent formulation and indeed that recent work on the modular hamiltonian in quantum field theory provides additional support for its underlying assumptions. The thermodynamic approach, on the other hand, seems to suffer from a difficulty in providing a self-consistent definition for what the appropriate entropy is going to be.
In the title of this work, we asked, “What is the entropy in entropic gravity?” We are now equipped to answer this question. In what we have called “holographic gravity,” the vacuum subtracted von Neumann entanglement entropy (the Casini entropy), evaluated on the null surfaces of the causal diamond, provides an appropriate formulation for an entropic treatment of gravitation. This can help guide further attempts to understand the underlying microscopic degrees of freedom giving rise to gravitation in general spacetime backgrounds.
… Read more at http://arxiv.org/pdf/1601.07558v1.pdf

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 http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.115.260602

Check also Sebastian Deffner’s Viewpoint: Exorcising Maxwell’s Demon at http://physics.aps.org/articles/v8/127

Read more at http://www.aalto.fi/en/current/news/2016-01-11/

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

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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.
…. Read more at http://arxiv.org/ftp/arxiv/papers/1512/1512.04981.pdf

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Equivalence of Quantum Heat Machines and Quantum-Thermodynamic Signatures

 (a) A two-level scheme of a four-stroke engine. (b) A two-particle scheme of a two-stroke engine. (c) A three-level scheme of a continuous engine

(a) A two-level scheme of a four-stroke engine. (b) A two-particle scheme of a two-stroke engine. (c) A three-level scheme of a continuous engine

Raam Uzdin, Amikam Levy, and Ronnie Kosloff
Quantum heat engines (QHE) are thermal machines where the working substance is a quantum object. In the extreme case, the working medium can be a single particle or a few-level quantum system. The study of QHE has shown a remarkable similarity with macroscopic thermodynamical results, thus raising the issue of what is quantum in quantum thermodynamics. Our main result is the thermodynamical equivalence of all engine types in the quantum regime of small action with respect to Planck’s constant. They have the same power, the same heat, and the same efficiency, and they even have the same relaxation rates and relaxation modes. Furthermore, it is shown that QHE have quantum-thermodynamic signature; i.e., thermodynamic measurements can confirm the presence of quantum effects in the device. We identify generic coherent and stochastic work extraction mechanisms and show that coherence enables power outputs that greatly exceed the power of stochastic (dephased) engines.
Read more at http://journals.aps.org/prx/pdf/10.1103/PhysRevX.5.031044

Read also: What is quantum in quantum thermodynamics?

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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…
… Read more at http://arxiv.org/pdf/1410.6965v1.pdf

Super-adiabatic quantum engines

cycle_srep06208-f1The practical untenability of the quasi-static assumption makes any realistic engine intrinsically irreversible and its operating time finite, thus implying friction effects at short cycle times.
An important technological goal is thus the design of maximally efficient engines working at the maximum possible power.
We show that, by utilising shortcuts to adiabaticity in a quantum engine cycle, one can engineer a thermodynamic cycle working at finite power and zero friction. Our findings are illustrated using a harmonic oscillator undergoing a quantum Otto cycle….
… Read more at www.nature.com

Read also: Physicists design zero-friction quantum engine