An exponential form of the normalized time correlation function

In the present work, a chain of the Zwanzig–Mori equations is considered for normalized time correlation functions (NTCFs). A solution to the chain of equations is derived under assumption that any NTCF has an exponential form. It is demonstrated that the solution obtained does not satisfy the condition that the NTCF is equal to unity at the initial moment of time. For this reason, exponential NTCFs are approximate, they meet an approximate dynamics. Exactly exponential dynamics is impossible.