  We introduce an extension of the generalised $T\bar{T}$-deformation described
by Smirnov-Zamolodchikov, to include the complete set of extensive charges. We
show that this gives deformations of S-matrices beyond CDD factors, generating
arbitrary functional dependence on momenta. We further derive from basic
principles of statistical mechanics the flow equations for the free energy and
all free energy fluxes. From this follows, without invoking the microscopic
Bethe ansatz or other methods from integrability, that the thermodynamics of
the deformed models are described by the integral equations of the
thermodynamic Bethe-Ansatz, and that the exact average currents take the form
expected from generalised hydrodynamics, both in the classical and quantum
realms.
