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Simplified disorder

Team from Campinas and the MIT draws up a method that facilitates the calculation of entropy

EDUARDO CESARThe spreading of a liquid: spontaneous movementEDUARDO CESAR

More than an obscure concept, disorder is a physical quantity that can be measured, in the same way as the length of a pencil. The apparent confusion that accompanies the prosaic spreading of coffee in a cup of milk is called entropy, nowadays calculated on a computer using at least 20 different approaches. As these techniques are complicated and laborious, a team from the State University of Campinas (Unicamp) and from the Massachusetts Institute of Technology (MIT), in the United States, created a simpler method that leads to the same results: it is Reversible Scaling (RS), which, according to its authors, goes so far as being 40 times quicker to calculate entropy and the free energy free for great temperature ranges.

Free energy is that portion of energy contained in a physical system that can be converted into useful work – for example, only a part of the chemical energy contained in a liter of gasoline is transformed into movement in an automobile. “The interest in calculating entropy and free energy is that they also signpost the way by which nature develops spontaneously”, says Alex Antonelli, from Unicamp’s Physics Institute, one of the authors of the program, jointly made with his former student Maurice de Koning, today at the MIT, and Sidney Yip, one of the pioneers in computer simulation in physical systems, also from the MIT.

In the case of water turning into ice, the free energy of the water is lower for the liquid state than for the solid state, at temperatures higher than 0° Celsius. But the situation is inverted at temperatures below this level – this is the reason why water freezes when cooled down to zero. “The state of lowest free energy always predominates”, says the researcher. There is also a delicate balance between internal energy and entropy – in other words, free energy – that determines the spatial structure of the proteins of any living being.

From cells to the heat of the Earth
The traditional method most used, Thermodynamic Integration, or TI, demands from five to ten simulations at a given temperature to get the entropy or the free energy at this given temperature. Supported by FAPESP, the recently created RS starts off with a specific temperature, from which one finds out the free energy, and changes it in a slow, dynamic way, with just one simulation – that is where the time saving comes from. “Nobody thought before of adopting this approach, because it was thought that it wouldn’t work”, says Antonelli. Dreamt up by Koning, RS was made public in 1999, in an article in Physical Review Letters. Adopted by such renowned researchers as chemist William Reinhardt, from University of Washington, it earned a detailed description in December 2001, in th eJournal of Chemical Physics. In January, Nature Materials published a three-page article on this new approach, signed by Yip.

RS is not a computer program, but a public domain method. For this reason, Antonelli reminds us, each researcher has to adapt it to his specific problems. For example, a group from Rio Grande do Sul is interested in using this approach to calculate the free energy of the ions (electrically charged atomic particles) that pass through cell membranes. RS may also be useful in studying the properties of materials, when simulation is the only way. Recently, with an approach that, according to Antonelli, could be done in ten times less time using RS, and team in Britain estimated the temperature of the liquid iron in the center of the Earth at about 6,500°C.

The project
Group of Electronic and Structural Properties of Metals and Semiconductors (nº 99/05157-6); Modality Regular line of research grants; Coordinator Alex Antonelli – Physics Institute at Unicamp; Investment R$ 25,599.18 and US$ 37,482.32