  The one-dimensional (1D) Hubbard model, describing electrons on a lattice
with an on-site repulsive interaction, provides a paradigm for the physics of
quantum many-body phenomena. Here by solving the thermodynamic Bethe ansatz
equations we study the universal thermodynamics, quantum criticality and
magnetism of the 1D attractive Hubbard model. We show that the compressibility
and the susceptibility of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO)-like
state obey simple additivity rules at low temperatures, indicating an existence
of two free quantum fluids. The magnetic properties, such as magnetization and
susceptibility, reveal three physical regions: quantum fluids at low
temperatures, a non-Fermi liquid at high temperatures and the quantum fluid to
non-Fermi liquid crossover in between. The lattice interaction is seen to
significantly influence the nature of the FFLO-like state in 1D. Furthermore,
we show that the dimensionless Wilson ratio provides an ideal parameter to map
out the various phase boundaries and to characterize the two free fluids of the
FLLO-like state. The quantum scaling functions for the thermal and magnetic
properties yield the same dynamic critical exponent $z=2$ and correlation
critical exponent $\nu=1/2$ in the quantum critical region whenever a phase
transition occurs. Our results provide a rigorous understanding of quantum
criticality and free fluids of many-body systems on a 1D lattice.
