In statistical physics, the principle of maximum entropy provides conditions on the singular behavior of thermodynamic functions near a critical point, in the form of inequalities for the critical-point exponents. Hadronic matter, when described by an exponentially rising density of states (dual resonance, statistical bootstrap models), exhibits critical behavior at a finite temperature T/sub c/. We calculate the basic critical-point exponents for such systems and investigate the range of validity of the corresponding inequalities.