  (abridged) We have studied the effects of electron-ion non-equipartition in
the outer regions of relaxed clusters for a wide range of masses in the
\LambdaCDM cosmology using one-dimensional hydrodynamic simulations. The
effects of the non-adiabatic electron heating efficiency, \beta, on the degree
of non-equipartition are also studied. Using the gas fraction f_gas = 0.17
(which is the upper limit for a cluster), we give a conservative lower limit of
the non-equipartition effect on clusters. Beyond the virial radius, the
non-equipartition effect depends rather strongly on \beta, and such a strong
dependence at the shock radius can be used to distinguish shock heating models
or constrain the shock heating efficiency of electrons. We have also studied
systematically the signatures of non-equipartition on X-ray and SZ observables.
We have calculated the effect of non-equipartition on the projected temperature
and X-ray surface brightness profiles using the MEKAL emission model. The
non-equipartition effect can introduce a ~10% bias in the projected temperature
at R_vir for a wide range of \beta. We also found that the effect of
non-equipartition on the projected temperature profiles can be enhanced by
increasing metallicity. We found that for our model in the \LambdaCDM Universe,
the integrated SZ bias, Y_{non-eq}/Y_{eq}, evolves slightly (at a percentage
level) with redshift, which is in contrast to the self-similar model in the
Einstein-de Sitter Universe. This may introduce biases in cosmological studies
using the f_gas technique. We discussed briefly whether the equipartition and
non-equipartition models near the shock region can be distinguished by future
radio observations with, for example, ALMA.
