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Simulations show that the geometric deformations induced by the metric tensor in case of a decrease in the inverse temperature are not reversible for an increase of the same amount, provided there is significant variation in the system's entropy: the process of taking a system from a lower entropy state A to a higher entropy state B and then bringing it back to A, induces a natural intrinsic one-way direction of evolution. In this context, Fisher curves resemble mathematical models of hysteresis in which the natural orientation is pointed by an arrow of time.<\/jats:p>","DOI":"10.1515\/mcma-2016-0107","type":"journal-article","created":{"date-parts":[[2016,5,27]],"date-time":"2016-05-27T10:03:04Z","timestamp":1464343384000},"page":"81-107","source":"Crossref","is-referenced-by-count":4,"title":["Information geometry, simulation and complexity in Gaussian random fields"],"prefix":"10.1515","volume":"22","author":[{"given":"Alexandre L.","family":"Levada","sequence":"first","affiliation":[{"name":"Computing Department, Federal University of S\u00e3o Carlos, S\u00e3o Carlos, SP, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2016,5,27]]},"reference":[{"key":"2023040101305239028_j_mcma-2016-0107_ref_000_w2aab2b8b8b1b7b1ab1ab1Aa","doi-asserted-by":"crossref","unstructured":"R. Albert and A. L. 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