Israeli researchers have succeeded in measuring the entropy (disorder) in complex systems

The method is expected to help researchers in a wide variety of fields, starting with the identification of gene mutations and ending with the design of new materials, which supercomputers have difficulty with

Researchers from Prof. Roi Beck-Barkai's laboratory at Tel Aviv University's School of Physics have developed a groundbreaking method for calculating entropy - the level of disorder of complex systems, a problem that has occupied scientists all over the world for years, and which even advanced supercomputers have had difficulty with. The new method is based on common software for compressing files such as ZIP, which are found in every computer and mobile phone today. According to Prof. Beck-Barkai "the importance of the method is its simplicity and accessibility, and it has many potential uses in a wide variety of fields: starting with the identification of proteins carrying mutations and ending with the development of new substances."

The research was led by PhD student Ram Avinari from Prof. Beck-Barkai's laboratory.

The article was recently published in the journal Physical Review Letters.

"Entropy is defined as the level of disorder of systems in nature," explains Prof. Beck-Barkai. "For example, a crystal, where every atom is in its place, has low entropy; On the other hand, a gas, where the atoms wander randomly in space, has a high entropy. Entropy is a very important measure in the study of different types of systems - starting with complex molecules of proteins, and ending with new materials that we develop for a variety of needs. But today's accepted research methods, which rely on computer simulations of physical processes, are unable to effectively provide a reliable measure of entropy. This is because the more complex the system is, such as a protein molecule, it has an infinite number of possible states in space, and even an advanced supercomputer will have difficulty calculating them all and determining the level of order in the system in a simulation. This problem has occupied the best scientists for many years, but so far no effective and satisfactory solution has been found."

Now researchers in Prof. Beck-Barkai's laboratory have found a groundbreaking, efficient and accessible solution to the difficult issue. They noticed that the equation used to determine entropy in physics is the same as the entropy equation from information theory, which plays a central role in common data compression programs found on every computer and smartphone, such as ZIP. "This algorithm constitutes an upper barrier that determines to what size the relevant file can be shrunk," says Prof. Beck-Barkai. "Actually, in the digital age, all documents, from photos and presentations to WORD documents, are being shrunk so that they take up less space on the computer or for the purpose of sending via the Internet. The data compression algorithm scans the file, and when it detects patterns that have already appeared before, it does not rewrite them but generates a reference to the previous mention. This way it saves space and the file is small. The more repetitions there are in the file, the more organized it is, and then the compressed file is smaller, and the entropy index of the information is also lower."

After noticing the connection between the data compression algorithm and the entropy equation, the researchers fed the results of physical computer simulations of complex systems into well-known compression software, which today is available for free on every computer and smartphone. The programs created compressed files from the data, and the researchers found that the size of the resulting file can be translated into an accurate measure of entropy. This is how they created for the first time a convenient and efficient tool for quantifying the entropy of extremely complex systems - from magnetic systems to protein molecules.

"The importance of our method is in its simplicity and accessibility," concludes Prof. Bek-Barkai. "This is real news for researchers in many fields - from biology and chemistry to physics, materials science and nanotechnology. For the first time, any researcher can quantify the entropy of complex systems easily and efficiently, on his personal computer and even on his mobile phone. A reliable and convenient solution, with many potential applications, has now been found for the problem that occupied the best minds. For example, using the new method it is possible to identify proteins with an abnormal folding form that causes the disease; to investigate self-assembly processes related to the production of innovative materials; and enable a better understanding of complex physical processes that are at the forefront of future technology."

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