Superfluid2 2009-05-09 09:38:02 2009-05-09 10:02:17 Definition supefluid $^3$He Cooper (electron) pairs long-range coupling superconductivity coupled boson systems quantum statistical theories quantum statistical mechanics A {\em superfluid} is described as a macroscopically coherent quantum system $S_F$ that exhibits `unusual' properties such as negligible losses or no resistance to flows. Therefore, it is defined as a phase that exhibits most unusual effects, previously considered to be anomalous from a thermodynamic viewpoint, that can be however explained in terms of quantum statistical theory/quantum statistical mechanics and long-range coherence of coupled boson systems. As an example, in a superconductor the long-ranged coupling of Cooper electron pairs form a superfluid that sustains very high electric currents without any significant heating of the metal. Liquid $^3$He is another example of a superfluid where the liquid flow can take place upwards in the absence of externally applied pressure and no apparent resistance to flow--no viscosity.