  The thermodynamic Bethe ansatz approach to the study of integrable quantum
field theories was introduced in the early 90s. Since then it has been known
that the thermodynamic Bethe ansatz equations can be recast in the form of
$Y$-systems. These $Y$-systems have a number of interesting properties, notably
in the high-temperature limit their solutions are constants from which the
central charge of the ultraviolet fixed point can be obtained and they are
typically periodic functions, with period proportional to the dimension of the
perturbing field. In this letter we discuss the derivation of $Y$-systems when
the standard thermodynamic Bethe ansatz equations are replaced by generalised
versions, describing generalised Gibbs ensembles. We shown that for many
integrable quantum field theories, there is a large class of distinct
generalised Gibbs ensembles which share the same $Y$-system.

High Energy Physics - Theory;Statistical Mechanics