  The relaxation function is the cornerstone to perform calculations in weakly
driven processes. Properties that such a function should obey are already
established, but the difficulty in its calculation is still an issue to be
overcome. In this work, I proposed a new method to determine such a function
for thermally isolated systems, based on a Hamilton's equations approach.
Observing that the microscopic relaxation function can be turned into a
canonical variable, one can choose the initial conditions of the solutions of
Hamilton's equations to avoid the calculation of the average in the initial
canonical ensemble. The unbearable example of the quartic oscillator is solved
to corroborate the method. Extensions to the quantum realm and stochastic
thermodynamics are mandatory.
