{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:35:29Z","timestamp":1760243729475,"version":"build-2065373602"},"reference-count":13,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2012,7,23]],"date-time":"2012-07-23T00:00:00Z","timestamp":1343001600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The socio-thermodynamics of a population of two competing species exhibits strong analogies with the thermodynamics of solutions and alloys of two constituents. In particular we may construct strategy diagrams akin to the phase diagrams of chemical thermodynamics, complete with regions of homogeneous mixing and miscibility gaps.<\/jats:p>","DOI":"10.3390\/e14071285","type":"journal-article","created":{"date-parts":[[2012,7,23]],"date-time":"2012-07-23T11:11:45Z","timestamp":1343041905000},"page":"1285-1295","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Socio-Thermodynamics\u2014Evolutionary Potentials in a Population of Hawks and Doves"],"prefix":"10.3390","volume":"14","author":[{"given":"Ingo","family":"M\u00fcller","sequence":"first","affiliation":[{"name":"Thermodynamics, Technical University Berlin, 10623, Berlin, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2012,7,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1038\/246015a0","article-title":"The logic of animal conflict","volume":"246","author":"Price","year":"1973","journal-title":"Nature"},{"key":"ref_2","unstructured":"Straffin, P.D. (1993). Game Theory and Strategy, New Mathematical Library, The Mathematical Association of America."},{"key":"ref_3","unstructured":"Dawkins, R. (1976). The Selfish Gene, Oxford University Press."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"389","DOI":"10.1007\/s001610200080","article-title":"Socio-thermodynamics\u2014Integration and segregation in a population","volume":"14","year":"2002","journal-title":"Continuum. Mech. Therm."},{"key":"ref_5","unstructured":"M\u00fcller, I. (2007). A History of Thermodynamics\u2014The Doctrine of Energy and Entropy, Springer."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Bakshi, B.R., Gutowski, T.G., and Sekulic, D.P. (2011). Thermodynamics and the Destruction of Resources, Cambridge University Press.","DOI":"10.1017\/CBO9780511976049"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"512","DOI":"10.1007\/BF02546843","article-title":"Binary alloys as a model for the multicultural society","volume":"43","author":"Mimkes","year":"1995","journal-title":"J. Therm. Anal."},{"key":"ref_8","unstructured":"We let the total number of N birds be unchanged from generation to generation."},{"key":"ref_9","unstructured":"Here and in the sequel we adopt the Stirling formula in order to replace factorials of large numbers: ln a! \u2248 a ln a \u2212 a."},{"key":"ref_10","unstructured":"This strategy was invented by the biologists J. Maynard-Smith and G.R. Price [1] and Dawkins [3] in order to show that a mixed population of two competing species may be evolutionarily stable. Here I modify the strategy of those biologists in a trivial manner by introducing the price \u03c4, which I consider as dimensionless. In anticipation of misunderstandings or criticism I say this: Dawkins does not consider eA in (6) as relevant, because he refuses the practicality of pacts or conspiracies which favour the gain for the population as a whole rather than the gain of the selfish individual. The relevance of eA requires enforcement of social measures to make the gain of the population a criterion for behaviour. We assume that such measures are agreed upon in the population."},{"key":"ref_11","unstructured":"\u03c4 = 1 is a reference price in which both strategies coincide, except for the grab-and-run feature of strategy B. Penalties for either fighting or posturing should never turn into rewards for whatever permissible value of \u03c4. This condition imposes an upper bound on \u03c4: 0 < \u03c4< 4.33. That constraint could be avoided, if we allowed non-linear penalty reductions which we do not do for the sake of simplicity."},{"key":"ref_12","unstructured":"If there were evolution, the phase fraction would shift to the abscissa of the maximum of pB over subsequent generations."},{"key":"ref_13","unstructured":"It is fortunate that (14) lends itself to such a simple graphical interpretation, since an analytic solution is impossible because of the ln-terms in the entropic part of pB(zH). Actually, however, in Figure 3 the influence of entropy is arbitrarily enhanced by a factor 2, because otherwise the concave parts of pB(zH) would not be sufficiently well pronounced to make the construction clear."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/14\/7\/1285\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:51:23Z","timestamp":1760219483000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/14\/7\/1285"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,7,23]]},"references-count":13,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2012,7]]}},"alternative-id":["e14071285"],"URL":"https:\/\/doi.org\/10.3390\/e14071285","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2012,7,23]]}}}