  A universal relation is established between the quantum work probability
distribution of an isolated driven quantum system and the Loschmidt echo
dynamics of a two-mode squeezed state. When the initial density matrix is
canonical, the Loschmidt echo of the purified double thermofield state provides
a direct measure of information scrambling and can be related to the analytic
continuation of the partition function. Information scrambling is then
described by the quantum work statistics associated with the time-reversal
operation on a single copy, associated with the sudden negation of the system
Hamiltonian.
