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/content/aip/journal/jcp/140/20/10.1063/1.4879553
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/content/aip/journal/jcp/140/20/10.1063/1.4879553
2014-05-22
2016-12-09

Abstract

It has recurrently been proposed that the Boltzmann textbook definition of entropy () =  ln Ω() in terms of the number of microstates Ω() with energy should be replaced by the expression examined by Gibbs. Here, we show that either is equivalent to 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 unfeasible and leads in general to temperatures that are inconsistent with the notions of hot and cold.

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