  This dissertation focuses on the calculation of transport coefficients in the
matter created in a relativistic heavy-ion collision after the chemical
freeze-out. This matter can be well approximated by a pion gas out of
equilibrium. We describe the theoretical framework to obtain the shear and bulk
viscosities, the thermal and electrical conductivities and the flavor diffusion
coefficients of a meson gas at low temperatures. To describe the interactions
of the degrees of freedom, we use effective field theories with chiral and
heavy quark symmetries. We introduce the unitarization methods in order to
obtain a scattering amplitude that satisfies the unitarity condition exactly.
We perform the calculation of the transport properties of the low temperature
phase of quantum chromodynamics -the hadronic medium- that can be used in the
hydrodynamic simulations of a relativistic heavy-ion collision and its
subsequent evolution. We show that the shear viscosity over entropy density
exhibits a minimum in a phase transition by studying this coefficient in atomic
Argon (around the liquid-gas phase transition) and in the linear sigma model in
the limit of large number of scalar fields (that presents a chiral phase
transition). Finally, we provide an experimental method to estimate the bulk
viscosity in relativistic heavy-ion collisions by performing correlations of
the fluctuating components of the stress-energy tensor.
