  It is demonstrated that the generic four-dimensional
Taub-Newman-Unti-Tamburino (Taub-NUT) spacetimes can be perfectly described in
terms of three or four different kinds of thermodynamic hairs: the Komar mass
($M = m$), the "angular momentum" ($J_n = mn$), the gravitomagnetic charge ($N
= n$), and/or the dual (magnetic) mass ($\widetilde{M} = n$). In other words,
the NUT charge is a thermodynamic multihair which means that it simultaneously
has both rotation-like and electromagnetic charge-like characteristics; this is
in sharp contrast with the previous knowledge that it has only one physical
feature, or that it is purely a single solution parameter. To arrive at this
novel result, we put forward a simple, systematic way to investigate the
consistent thermodynamic first law and Bekenstein-Smarr mass formulas of all
four-dimensional spacetimes that contain a nonzero NUT charge, facilitated by
first deriving a meaningful Christodoulou-Ruffini-type squared-mass formula. In
this way, not only can the elegant Bekenstein-Hawking one-quarter area-entropy
relation be naturally restored in the Lorentzian and Euclidian sectors of
generic Taub-NUT-type spacetimes without imposing any constraint condition, but
also the physical meaning of the NUT parameter as a poly-facet can be
completely clarified in the thermodynamic sense for the first time.
