 where the symbol ‘lim’ (from latin ‘limes’, meaning border or limit) indicates that we are letting time tend towards infinity (in mathematical symbols: \(\infty)\). One point deserves special attention, since it will become crucial later on: the presence of \(x_0\) in the above expression. Time averages depend on where the system starts; i.e., they depend on the initial condition. If the process starts in a different state, the time average may well be different.