  Nonclassicality of temporal correlations pertaining to noncommutative
sequential measurements is defined through the violation of macrorealistic
inequalities, known as Leggett-Garg inequalities (LGI). We investigate the
energy cost of the process associated with the Leggett-Garg test in the context
of noiseless and Markovian noise for arbitrary initial states. We prove that in
noiseless and in certain noisy scenarios, the maximal violations of LGI under
the energy constraint occurs when the average energy of the process is equal to
the negative of the energy of the initial state. Such a dependence of LGI on
the choice of the initial state is not seen in the unconstrained case.
Moreover, we find that in the presence of a moderate amount of Markovian noise,
the amount of violation of LGI remains almost unaltered with a suitable choice
of the evolution and dephasing operators in the neighborhood of the maximal
violation line, thereby showing the robustness of temporal correlations under
environmental effects.
