Aside

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…
Read more at https://arxiv.org/ftp/arxiv/papers/1605/1605.06969.pdf

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

The Enigma of Entropy

entropyDeepak Dhar
One of the most mysterious of laws of nature is the second law of thermodynamics.
There are several equivalent formulations of One of the most mysterious of laws of nature is the second law of thermodynamics. There are several equivalent formulations of this law. For our present discussion, it is enough to take the Clausius formulation that says that for an isolated system evolving in time, the entropy cannot decrease.
Many of you have encountered this in your B.Sc. textbooks already. Let me explain my reasons for calling it enigmatic. I do not have any answers. I just want to say why I think that it is an interesting question.
Let me explain myself using a parable. A foreign scientist is visiting a laboratory in China.
In the day time, he discusses his work with his hosts, and in the evenings, he has to find some place to eat. Unfortunately, he knows no Chinese….
Read more: http://arxiv.org/pdf/1301.1892v1.pdf

Entropy-based Tuning of Musical Instruments

Typical tuning curve of a piano. The plot shows how
much the fundamental frequency of each note deviates from the equal-tempered scale

Haye Hinrichsen
The human sense of hearing perceives a combination of sounds ‘in tune’ if the corresponding harmonic spectra are correlated, meaning that the neuronal excitation pattern in the inner ear exhibits some kind of order. Based on this observation it is suggested that musical instruments such as pianos can be tuned by minimizing the Shannon entropy of suitably preprocessed Fourier spectra. This method reproduces not only the correct stretch curve but also similar pitch fluctuations as in the case of high-quality aural tuning….
Read more: http://arxiv.org/pdf

The thermodynamic meaning of negative entropy

Erase entangled memory to cool a computer
Imagine cooling a supercomputer not with fans or freezers, but by deleting some of its memory. New calculations show that this is possible, provided some of the bits that make up the computer’s memory are “entangled”– a spooky property that can link two quantum systems, no matter how far apart they sit in physical space.
The notion of cooling by erasure seemingly violates a principle articulated by physicist Rolf Landauer in 1961. He showed that erasing information is akin to a decrease in entropy or disorder. As entropy overall must always increase, the deletion of bits must therefore be accompanied by an increase in the entropy of the surroundings, which manifests itself as heat.
The heat produced by a computer today is mainly due to processing inefficiencies, and while these can be reduced, Landauer’s insight implies a fundamental limit on how much you can reduce the heat generated by computing.
Now, Lídia del Rio of the Swiss Federal Institute of Technology in Zurich and colleagues have shown that quantum entanglement provides a way to sneak around Landauer’s law.

Entropy dip

To understand how this might work, consider two people who are each trying to erase a string of bits in computer memory, which can exist either as 1s or 0s. One of the pair has no knowledge of the stored bits, so to ensure they get erased, he or she must always reset them to “0”, regardless of their original content. The second person, however, knows the content of the string and so need only reset those bits that are 1s.
In this situation, the first person has to do more work on average to erase the string than the second. As a result, the “conditional entropy” of the memory is said to be lower for the first person than the second.
Now imagine that the memory bits to be erased are entangled with other objects. In such a system, observing or determining the state of one part immediately fixes the state of the other. So an observer who has access to the entangled objects could know even more about the memory than would be possible otherwise, causing the conditional entropy of the system to dip and become negative when the memory is erased.

Weirdness at work

Del Rio and colleagues have shown mathematically that this negative conditional entropy is the equivalent of extracting heat from the surroundings, or cooling.
The team envisages future computers containing entangled systems of this kind. Deletion of some of a computer’s memory should lead to cooling. “If you go to this entangled level of operations, then you will be at the limit of what physics allows you to do,” says team member Vlatko Vedral of the University of Oxford.
This does not violate the laws of thermodynamics: there is still an overall increase in entropy because energy is needed to create the entangled system initially.
At the moment, entangled states are not easy to work with: they require extreme cooling and are notoriously fragile. Still, Robert Prevedel of the University of Waterloo, Ontario, Canada, who was not involved in the work, is impressed by the idea. “This demonstrates that the weird features of the quantum world are not only useful as an informational resource, but can actually be used to generate some real, physical work,” he says.
Journal Reference: Nature, DOI: 10.1038/nature10123
http://www.newscientist.com/article/dn20544-erase-entangled-memory-to-cool-a-computer.html
Read more in “Erasing data could keep quantum computers cool