1307.6681 (E. Canessa)
E. Canessa
We postulate the log-periodic master equation for a universal, probabilistic description of entropy $S = - (k/a) \sum_{i=1}^{N} p_{i} \sin(a \ln p_{i})$, with $N$ the total number of system states and $p_{i}$ the associated probabilities. We discuss its properties, and make a connection with the non-extensive Tsallis, R\'{e}nyi, Boltzmann-Gibbs and Shannon entropies as special limiting cases. Log-periodicity in $S$, concavity lost, and non-additivity are manifested by increasing the value of the coefficient $a$, which sets the variations with respect to the behavior of the monotonic Gibbs entropy function. It is argued that an oscillatory regime for $S$ could in principle be understood in terms of a linear time-dependent behavior for the associated probabilities in analogy with a spring system gaining momentum from the surroundings.
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http://arxiv.org/abs/1307.6681
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