Using the assumption that thermodynamic systems evolve towards
Gibbs states, i.e. states with a well defined temperature, statistical
mechanics and thermodynamics have been amazingly successful in
explaining a wide range of physical phenomena. In stark contrast to this
strong justification by corroboration of these theories, the question of
whether and how the methods of statistical mechanics and thermodynamics
can be justified microscopically was still wide open until recently.
With new mathematical tools from quantum information theory becoming
available, there has been a renewed effort to settle this old question.
I will present and discuss a necessary and a sufficient condition for
the emergence of Gibbs states from the unitary dynamics of quantum
mechanics and show how these new insights into the process of
equilibration and thermalization can be used to design a quantum
algorithm that prepares thermal states on a quantum computer/simulator.