  To understand under which conditions thermodynamics emerges from the
microscopic dynamics is the ultimate goal of statistical mechanics. Despite the
fact that the theory is more than 100 years old, we are still discussing its
foundations and its regime of applicability. A point of crucial importance is
the definition of the notion of thermal equilibrium, which is given as the
state that maximises the von Neumann entropy. Here we argue that it is
necessary to propose a new way of describing thermal equilibrium, focused on
observables rather than on the full state of the quantum system. We
characterise the notion of thermal equilibrium, for a given observable, via the
maximisation of its Shannon entropy and highlight the thermal properties that
such a principle heralds. The relation with Gibbs ensembles is brought to
light. Furthermore, we apply such a notion of equilibrium to a closed quantum
systems and prove that there is always a class of observables which exhibits
thermal equilibrium properties and we give a recipe to explicitly construct
them. Eventually, we bring to light an intimate connection of such a principle
with the Eigenstate Thermalisation Hypothesis.
