Hadron condensation before the Hagedorn temperature

A Bose hadron gas in a large volume is considered, which obeys the bootstrap equation only in small regions of 1 fm3 size, but behaves with normal clusterization otherwise and consequently has the ideal-gas limiting behaviour for low density. In general, the relativistic chemical potential must then be introduced and energy density and temperature are independent variables. The temperature T is bounded by Tsub(deg). The volume simply appears as a factor in the grand potential Ω(T, V, z) and the derivative deltaΩ/deltaT maintains the Hagedorn singularity for T→Tsub(deg). The phenomenon of condensation takes place for T(<=)Tsub(e)(<=)Tsub(deg) for density ω high enough. The difference from the ideal-gas Bose condensation (extrapolated to infinitely large energy density) is that in the bootstrap Bose system the range of values 0(<=)zeta(<=)1 corresponds to a temperature interval Tsub(e)(<=)T(<=)Tsub(deg), which vanishes as 1/ω2 for large ω. Moreover, the system has the typical bootstrap fluctuations at T approximately Tsub(deg). In the present treatment such fluctuations are between ''gas'' and ''liquid'' phases