We investigate the effects of the timescale of motion on the shape of energy landscapes. The distinction between the free-energy landscape and the potential of mean force is clarified. The former is related to a thermal equilibrium distribution for chosen coordinates, whereas the latter is determined by the mean force exerted on the coordinates in the equilibrium. It is found that the condition for these two energy landscapes to be the same is the constancy of the mean square velocity with respect to the position coordinate. However, even when the condition holds for the chosen coordinates, as the timescale of observation increases, the averaging effect causes a decrease in the mean square velocity nonuniformly in the configuration space, resulting in a larger distinction between the free-energy landscape and the potential of mean force. The results are expected to provide an important basis for the study of long time scale phenomena in large systems. [15][16][17]. Two important roles of the energy landscape can be pointed out. One is that the gradients of the energy landscape with respect to the coordinates give the forces in the directions of those coordinates by which the motion of the system is driven on the landscape. Thus, chemical reactions can be imagined as a point mass moving on the energy surface drawn in the configuration space, and their rate constants can also be calculated from the information of the energy surface [8,[18][19][20][21]. Also, phenotypic diversification of cells can be modeled as the motion of marbles on Waddington's landscape [15][16][17].The other role of the energy landscape is that the probability distribution at the stationary state is given by the energy landscape through the Boltzmann factor. Thus, the stable structures of proteins can be predicted as minima of the free-energy landscape, and it is possible to elucidate specific interactions that give rise to the stable structures [7,[22][23][24]. It is, in a sense, surprising that these two different concepts, one being a dynamical concept of force and the other being a statistical distribution, can be given by the same energy function.Large complex systems involve a huge number of degrees of freedom and experience the underlying energy landscapes with hierarchical time and space scales. When some, but not all, degrees of freedom are considered to have reached a stationary distribution, it is natural to represent the energy landscape with a smaller set of degrees of freedom by averaging all the others over the stationary distribution. Moreover, due to * skawai@es.hokudai.ac.jp limited experimental time resolution or an interest in slow motions, e.g., relevant to biological functions, rather than the full details of motion over all the timescales, we are often interested in investigating the behavior of physical quantities over long timescales. What kinds of energy landscape are seen at different timescales in such reduced systems is an intriguing subject. It is even not clear whether the two different roles mentioned above c...