# Communication: system-size scaling of Boltzmann and alternate Gibbs entropies.

@article{Vilar2014CommunicationSS, title={Communication: system-size scaling of Boltzmann and alternate Gibbs entropies.}, author={Jose M. G. Vilar and J. Miguel Rub{\'i}}, journal={The Journal of chemical physics}, year={2014}, volume={140 20}, pages={ 201101 } }

It has recurrently been proposed that the Boltzmann textbook definition of entropy S(E) = k ln Ω(E) in terms of the number of microstates Ω(E) with energy E should be replaced by the expression S(G)(E) = k ln Σ(E' < E)Ω(E') examined by Gibbs. Here, we show that SG either is equivalent to S in the macroscopic limit or becomes independent of the energy exponentially fast as the system size increases. The resulting exponential scaling makes the realistic use of SG unfeasible and leads in general…

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