The so-called ergodic theorem formulates a fundamental physical principle relating to the behavior of dynamical systems. Essentially the theorem states that in a multiparticle system each individual particle behaves just as "chaotically" as does the system as a whole. In other words, one can extrapolate from the behavior of a single element to that of the whole system. Strangely enough, in spite of its wide-ranging implications, the theorem has not been rigorously tested experimentally. A collaborative effort mounted by Professor Christoph Bruchle's team in the Department of Chemistry at LMU Munich and Professor Jrg Krger's group at Leipzig University has now confirmed the validity of the theorem by measuring the diffusive behavior of ensembles of particles and the trajectories of single molecules in the same system. Using fluorescent molecules as tracers and high-resolution imaging methods, the LMU investigators were able to track the paths of individual molecules, while the Leipzig group studied the collective behavior of the whole ensemble. "It will be very interesting to take a closer look at systems that do not conform to the tenets of the ergodic theorem and to determine the reasons for their aberrant behavior," says Bruchle.
The term "diffusion" refers to the random motion of particles, such as atoms and molecules, under the influence of thermal energy. This physical process is an essential component of innumerable phenomena in nature, and also plays a crucial role in many technological procedures. For instance, in virtually all chemical reactions, diffusion is responsible for bringing reactants sufficiently close together to enable them to react at all. It is generally accepted that the ergodic theorem is applicable to the dynamics of diffusive processes. The theory basically states that repeated measurements of a given variable such as the distance covered by a particle in a given time interval should yield the same average value as a singl
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