  In the context of nonequilibrium quantum thermodynamics, variables like work
behave stochastically. A particular definition of the work probability density
function (pdf) for coherent quantum processes allows the verification of the
quantum version of the celebrated fluctuation theorems, due to Jarzynski and
Crooks, that apply when the system is driven away from an initial equilibrium
thermal state. Such a particular pdf depends basically on the details of the
initial and final Hamiltonians, on the temperature of the initial thermal state
and on how some external parameter is changed during the coherent process.
Using random matrix theory we derive a simple analytic expression that
describes the general behavior of the work characteristic function $G(u)$,
associated with this particular work pdf for sudden quenches, valid for all the
traditional Gaussian ensembles of Hamiltonians matrices. This formula well
describes the general behavior of $G(u)$ calculated from single draws of the
initial and final Hamiltonians in all ranges of temperatures.
