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We establish their numerical equivalence in several cases, which includes the most important case when the thermodynamic entropy is a state function. We discuss various interesting aspects of the two entropies and show that the number of microstates in the Boltzmann entropy includes all possible microstates of non-zero probabilities even if the system is trapped in a disjoint component of the microstate space. We show that negative thermodynamic entropy can appear from nonnegative statistical entropy.<\/jats:p>","DOI":"10.3390\/e17020710","type":"journal-article","created":{"date-parts":[[2015,2,5]],"date-time":"2015-02-05T10:54:42Z","timestamp":1423133682000},"page":"710-754","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["On Equivalence of Nonequilibrium Thermodynamic and Statistical Entropies"],"prefix":"10.3390","volume":"17","author":[{"given":"Purushottam","family":"Gujrati","sequence":"first","affiliation":[{"name":"Department of Physics, The University of Akron, Akron, OH 44325, USA"},{"name":"Department of Polymer Science, The University of Akron, Akron, OH 44325, USA\u00a0"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2015,2,5]]},"reference":[{"key":"ref_1","unstructured":"Clausius, R. (1879). 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