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Entropy 2018, 20(2), 115; https://doi.org/10.3390/e20020115

Entropy Affects the Competition of Ordered Phases

1
Department of Theoretical Physics, Faculty of Natural Sciences, Budapest University of Technology and Economics, Budafoki út 8, H-1111 Budapest, Hungary
2
Institute of Technical Physics and Materials Science, Centre for Energy Research, Hungarian Academy of Sciences, P.O. Box 49, H-1525 Budapest, Hungary
*
Author to whom correspondence should be addressed.
Received: 5 January 2018 / Revised: 2 February 2018 / Accepted: 8 February 2018 / Published: 10 February 2018
(This article belongs to the Special Issue Information Theory in Game Theory)
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Abstract

The effect of entropy at low noises is investigated in five-strategy logit-rule-driven spatial evolutionary potential games exhibiting two-fold or three-fold degenerate ground states. The non-zero elements of the payoff matrix define two subsystems which are equivalent to an Ising or a three-state Potts model depending on whether the players are constrained to use only the first two or the last three strategies. Due to the equivalence of these models to spin systems, we can use the concepts and methods of statistical physics when studying the phase transitions. We argue that the greater entropy content of the Ising phase plays an important role in its stabilization when the magnitude of the Potts component is equal to or slightly greater than the strength of the Ising component. If the noise is increased in these systems, then the presence of the higher entropy state can cause a kind of social dilemma in which the players’ average income is reduced in the stable Ising phase following a first-order phase transition. View Full-Text
Keywords: evolutionary games; lattice systems; potential games; phase transitions evolutionary games; lattice systems; potential games; phase transitions
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Király, B.; Szabó, G. Entropy Affects the Competition of Ordered Phases. Entropy 2018, 20, 115.

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