Forum for Science, Industry and Business

Sponsored by:     3M 
Search our Site:

 

UGA research may lead to reassessment of some foundations of statistical mechanics

15.03.2007
There are probably more molecules in your den than there are stars in the universe. When studying numbers so vast, researchers had to find a way to make large-scale predictions based on the study of microscopic properties. That field of inquiry is called statistical mechanics, and it is an important tool in explaining how the world works.

A new research paper, just published in the online version of the journal Physical Review Letters by M. Howard Lee, Regents Professor of Physics at the University of Georgia, however, may lead to a reassessment of some foundations of statistical mechanics, according to its author.

“Reassessing old problems with new tools is always a challenge,” said Lee. “But it is a challenge that has been rewarding.”

At the heart of Lee’s new research is the work of two giants of physics and mathematics, Ludwig Boltzmann and George David Birkhoff and a hypothesis one proposed and the other proved. It is the story of a difficult and intricate theorem that remains important in using microscopic pictures to understand large-scale systems.

Boltzmann was a 19th century Austrian physicist and one of the founders of statistical mechanics. He proposed what came to be called the Ergodic Hypothesis: A time average is equal to an ensemble average. This elegant idea allowed scientists to compute accurate thermodynamic functions without having to examine how particles act and change over time.

It became one of the foundations of statistical mechanics, but actually proving Bolzmann’s hypothesis turned out to be a classically intractable problem, until Birkhoff, an American mathematician, came along. But while his proof seemed to work in the field of mathematics, it never satisfied physicists, who considered it far too abstract.

Lee’s paper in Physical Review Letters proposes a new solution to the problem that has perplexed researchers since Birkhoff’s solution some 70 years ago.

“Proving Bolzmann’s hypothesis is extremely difficult, because one must first solve the equation of motion, which is a daunting task in itself,” said Lee. “As a result, most people have come to accept the hypothesis despite occasional evidence to the contrary.”

In 2001, Lee laid the groundwork for testing the hypothesis by using a technique he had developed to help solve another problem in 1982 when he found an exact, general and practical solution to one of the most important problems in statistical physics. The problem was how to solve the so-called "Heisenberg equation of motion," which yields the response of a system to an external probe

While another scientist solved the problem first, Lee went about it in different way, one that provided for the first time a theory from which one could actually calculate. Lee’s work on that problem has had a tremendous impact on statistical mechanics, as evidenced by nearly 600 citations since its publication 25 years ago.

When a colleague suggested that Lee use this mathematical tool, which he calls an “ergometer,” to probe Birkhoff’s solution to Bolzmann’s hypothesis, a light bulb went off. This might be a way to take Birkhoff from mathematics into the very different realm of physics.

“To make sense of Birkhoff’s Theorem, let’s say that being Ergodic means being able to walk on land,” said Lee. “In this analogy, Birkhoff says that there is an island, but he doesn’t say how large or small the island is. It could be as small as an islet or as large as a continent. To physicists, it’s critical to know how large that island is.”

Lee then used his ergometer to help determine the boundaries and therefore the size of the “island.” In the Physical Review Letters paper, Lee examined where Birkhoff’s Theorem is violated and extracted from it the underlying physical basis for it.

“Establishing this connection puts Birkhoff’s Theorem on a physical terrain, enabling us to begin the mapping process of that island, and this paper is the start of that work,” said Lee.

It will also allow physicists to understand how widely valid Boltzmann’s Hypothesis actually is and help researchers in assessing the entire foundations of statistical mechanics.

M. Howard Lee | EurekAlert!
Further information:
http://www.uga.edu
http://www.uga.edu/news/artman/publish/070307statisticalMechanics.shtml

More articles from Physics and Astronomy:

nachricht Tracing aromatic molecules in the early universe
23.03.2017 | University of California - Riverside

nachricht New study maps space dust in 3-D
23.03.2017 | DOE/Lawrence Berkeley National Laboratory

All articles from Physics and Astronomy >>>

The most recent press releases about innovation >>>

Die letzten 5 Focus-News des innovations-reports im Überblick:

Im Focus: Giant Magnetic Fields in the Universe

Astronomers from Bonn and Tautenburg in Thuringia (Germany) used the 100-m radio telescope at Effelsberg to observe several galaxy clusters. At the edges of these large accumulations of dark matter, stellar systems (galaxies), hot gas, and charged particles, they found magnetic fields that are exceptionally ordered over distances of many million light years. This makes them the most extended magnetic fields in the universe known so far.

The results will be published on March 22 in the journal „Astronomy & Astrophysics“.

Galaxy clusters are the largest gravitationally bound structures in the universe. With a typical extent of about 10 million light years, i.e. 100 times the...

Im Focus: Tracing down linear ubiquitination

Researchers at the Goethe University Frankfurt, together with partners from the University of Tübingen in Germany and Queen Mary University as well as Francis Crick Institute from London (UK) have developed a novel technology to decipher the secret ubiquitin code.

Ubiquitin is a small protein that can be linked to other cellular proteins, thereby controlling and modulating their functions. The attachment occurs in many...

Im Focus: Perovskite edges can be tuned for optoelectronic performance

Layered 2D material improves efficiency for solar cells and LEDs

In the eternal search for next generation high-efficiency solar cells and LEDs, scientists at Los Alamos National Laboratory and their partners are creating...

Im Focus: Polymer-coated silicon nanosheets as alternative to graphene: A perfect team for nanoelectronics

Silicon nanosheets are thin, two-dimensional layers with exceptional optoelectronic properties very similar to those of graphene. Albeit, the nanosheets are less stable. Now researchers at the Technical University of Munich (TUM) have, for the first time ever, produced a composite material combining silicon nanosheets and a polymer that is both UV-resistant and easy to process. This brings the scientists a significant step closer to industrial applications like flexible displays and photosensors.

Silicon nanosheets are thin, two-dimensional layers with exceptional optoelectronic properties very similar to those of graphene. Albeit, the nanosheets are...

Im Focus: Researchers Imitate Molecular Crowding in Cells

Enzymes behave differently in a test tube compared with the molecular scrum of a living cell. Chemists from the University of Basel have now been able to simulate these confined natural conditions in artificial vesicles for the first time. As reported in the academic journal Small, the results are offering better insight into the development of nanoreactors and artificial organelles.

Enzymes behave differently in a test tube compared with the molecular scrum of a living cell. Chemists from the University of Basel have now been able to...

All Focus news of the innovation-report >>>

Anzeige

Anzeige

Event News

International Land Use Symposium ILUS 2017: Call for Abstracts and Registration open

20.03.2017 | Event News

CONNECT 2017: International congress on connective tissue

14.03.2017 | Event News

ICTM Conference: Turbine Construction between Big Data and Additive Manufacturing

07.03.2017 | Event News

 
Latest News

When Air is in Short Supply - Shedding light on plant stress reactions when oxygen runs short

23.03.2017 | Life Sciences

Researchers use light to remotely control curvature of plastics

23.03.2017 | Power and Electrical Engineering

Sea ice extent sinks to record lows at both poles

23.03.2017 | Earth Sciences

VideoLinks
B2B-VideoLinks
More VideoLinks >>>