  This paper investigates applicability of thermodynamic concepts and
principles to competitive systems. We show that Tsallis entropies are suitable
for characterisation of systems with transitive competition when mutations
deviate from Gibbs mutations. Different types of equilibrium in competitive
systems are considered and analysed. As competition rules become more and more
intransitive, thermodynamic analogies are eroded and the behaviour of the
system can become complex. This work analyses the phenomenon of punctuated
evolution in the context of the competitive risk/benefit dilemma.
