Propagation of "heat" in hadronic matter

We investigate the space-time evolution of a local excitation in hadronic matter (h.m.) in connection with the establishment of local thermodynamical equilibrium as assumed in statistical and hydrodynamical models. After a critical discussion of the concept of instantaneous equilibrium, we point out that peripheral reactions are a particularly useful source of information for the study of the fate of an excitation in h.m. We consider a local excitation ("hot spot") corresponding to a pre-equilibrium phase and which is created in peripheral inelastic reactions with $m_{\pi }\ll q\ll p_i$, where $p_i$ is the incoming momentum of the projectile and $q$ the momentum transfer. By solving the diffusion equation we obtain the distribution of the temperature field in the excited target (projectile) and compute all the relevant physical quantities such as average momenta of secondaries, multiplicities, and mass and energy distributions in semi-inclusive peripheral reactions. It turns out that these quantities have a pronounced angular dependence leading to an asymmetry in these observables. The measurement of this asymmetry can provide information on the constants of h.m. We also discuss how large-$p_{\perp }$ events observed in the CERN ISR energy range might be due to pre-equilibrium emission in close analogy to pre-equilibrium nuclear decay.