  We will discuss various aspects of thermalization, chaos and hydrodynamics in
one dimensional classical Hamiltonian systems. We study two problems.
  First, we will revisit the Fermi-Pasta-Ulam-Tsingou (FPUT) problem in order
to understand what thermalization is and discuss what leads the system starting
from a typical initial condition to a thermal state. Here we discuss the
various possibilities like the role of averaging, the choice of observables,
the choice of initial conditions and the role of chaos in thermalization.
  Then, we study the evolution of a blast wave in an alternate mass hard
particle (AHP) gas and study the evolution of conserved fields in the system at
short times. We find a good agreement with the Taylor-von Neumann-Sedov (TvNS)
solution, which was studied during the Second World War in the context of
atomic explosions, everywhere except near the core of the blast. We then model
this behaviour by using the Navier-Stokes-Fourier (NSF) equations.
