Multimode fibres (MMFs) have recently demonstrated a great potential towards discovering numerous new and complex processes that have never been observed, so far [1]. Among others, Kerr self-cleaning has unveiled the ability of graded-index (GRIN) fibres to produce a quasi-single-mode beam, despite the incoherent multimode propagation involving a large number of modes [2]. A clean beam with its improved brightness can then be obtained at the output of the GRIN MMFs. This phenomenon is enabled by the combined effect of self-imaging and Kerr nonlinearity, followed by a nonlinear nonreciprocity of the mode coupling process. This high-intensity self-transformation can also be described by a thermodynamic approach, whenever a large number of modes is involved [3–4].