  We establish through analytical and numerical studies of thermodynamic
quantities for noninteracting atomic gases that the isotropic three-dimensional
spin-orbit coupling, the Weyl coupling, induces interaction which counters
"effective" attraction (repulsion) of the exchange symmetry present in
zero-coupling Bose (Fermi) gas. The exact analytical expressions for the grand
potential and hence for several thermodynamic quantities have been obtained for
this purpose in both uniform and trapped cases. It is enunciated that many
interesting features of spin-orbit coupled systems revealed theoretically can
be understood in terms of coupling-induced modifications in statistical
interparticle potential. The temperature-dependence of the chemical potential,
specific heat and isothermal compressibility for a uniform Bose gas is found to
have signature of the incipient Bose-Einstein condensation in very weak
coupling regime although the system does not really go in the Bose-condensed
phase. The transition temperature in harmonically trapped case decreases with
increase of coupling strength consistent with the weakening of the statistical
attractive interaction. Anomalous behavior of some thermodynamic quantities,
partly akin to that in dimensions less than two, appears for uniform fermions
as soon as the Fermi level goes down the Dirac point on increasing the coupling
strength. It is suggested that the fluctuation-dissipation theorem can be
utilized to verify anomalous behaviors from studies of long-wavelength
fluctuations in bunching and antibunching effects.
