  We consider the problem of keeping an arbitrary state $\rho_s$ out of thermal
equilibrium. We find that counter-acting thermalisation using only a resource
system which is in a stationary state at the initial time and a system-resource
interaction that preserves the global energy is possible if and only if the
target state $\rho_s$ is block-diagonal in the eigenbasis of the system's
Hamiltonian $H_s.$ As a consequence, we compute the extra work the operator
must provide by tuning the resource-system interaction to overcome this
constraint. This quantity, which is interpreted as the work needed to preserve
the coherences in the state, can be expressed in terms of the target state
$\rho_s$ and the thermal equilibrium state $\rho_{\beta},$ and it is
proportional to the symmetrized relative entropy between $\rho_s$ and
$\rho_{\beta}.$
