{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,7]],"date-time":"2025-02-07T05:24:50Z","timestamp":1738905890551,"version":"3.37.0"},"reference-count":34,"publisher":"World Scientific Pub Co Pte Ltd","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Open Syst. Inf. Dyn."],"published-print":{"date-parts":[[2008,12]]},"abstract":"<jats:p>The notion of utility maximising entropy (u-entropy) of a probability density, which was introduced and studied in [37], is extended in two directions. First, the relative u-entropy of two probability measures in arbitrary probability spaces is defined. Then, specialising to discrete probability spaces, we also introduce the absolute u-entropy of a probability measure. Both notions are based on the idea, borrowed from mathematical finance, of maximising the expected utility of the terminal wealth of an investor. Moreover, u-entropy is also relevant in thermodynamics, as it can replace the standard Boltzmann-Shannon entropy in the Second Law. If the utility function is logarithmic or isoelastic (a power function), then the well-known notions of Boltzmann-Shannon and R\u00e9nyi relative entropy are recovered. We establish the principal properties of relative and discrete u-entropy and discuss the links with several related approaches in the literature.<\/jats:p>","DOI":"10.1142\/s1230161208000213","type":"journal-article","created":{"date-parts":[[2008,12,29]],"date-time":"2008-12-29T09:49:04Z","timestamp":1230544144000},"page":"303-327","source":"Crossref","is-referenced-by-count":0,"title":["Relative and Discrete Utility Maximising Entropy"],"prefix":"10.1142","volume":"15","author":[{"given":"Grzegorz","family":"Hara\u0144czyk","sequence":"first","affiliation":[{"name":"Institute of Mathematics, Jagiellonian University, \u0141ojasiewicza 6, 30\u2013348 Krak\u00f3w, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wojciech","family":"S\u0142omczy\u0144ski","sequence":"additional","affiliation":[{"name":"Institute of Mathematics, Jagiellonian University, \u0141ojasiewicza 6, 30\u2013348 Krak\u00f3w, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tomasz","family":"Zastawniak","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of York, Heslington, York YO10 5DD, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2012,1,25]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02192655"},{"key":"rf2","unstructured":"J.\u00a0Acz\u00e9l, Uncertainty in knowledge-based systems (Paris, 1986), Lecture Notes in Comput. 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