Abstract

If the sum of two time-dependent functions is less or equal a constant, and the infinite-time average of one of these functions is zero then the infinite time average of the other function is bounded from above by this constant. Under very mild assumptions, the infinite-time average of the Lie derivative of any function, or functional, of the state of a dynamical system is zero. Hence the Lie derivative of any such “auxiliary” function(al) can be added to the observable for which the bound for infinite-time average is sought, and then the bound can be optimised over the auxiliary function(al). In the last few years this simple idea received a fair amount of attention. In the talk the recent progress will be reviewed with a focus on combining the benefits of this approach and the experience accumulated in studies based on the famous background flow method.