  Contrary to many other translationally invariant one-dimensional models, the
low-temperature phase for an attractively interacting one-dimensional Bose-gas
(a quantum bright soliton) is stable against thermal fluctuations. However,
treating the thermal properties of quantum bright solitons within the canonical
ensemble leads to anomalous fluctuations of the total energy that indicate that
canonical and micro-canonical ensembles are not equivalent. State-of-the-art
experiments are best described by the micro-canonical ensemble, within which we
predict a co-existence between single atoms and solitons even in the
thermodynamic limit - contrary to strong predictions based on both the Landau
hypothesis and the canonical ensemble. This questions the use of temperatures
to describe state-of-the-art bright soliton experiments that currently load
Bose-Einstein condensates into quasi-one-dimensional wave guides without adding
contact to a heat bath.
