The entropic analysis of extended system helps to find realistic
models of extended spatiotemporal systems. The analysis is especially
powerful in cases where one can coarse-grain the phase space by physical
observation and/or assumptions. We extend the coarse graining from
the phase space as well to the time domain by applying physically motivated 
filtering techniques. The entropy is calculated by the powerful method of 
the exit-times and compared with conventional results. We investigate 
is a simplified model of the gulf stream with special emphasis of mixing 
effects between the different gulf stream regions.  Possible further 
applications are mixing between distinct oceanographic regions or the 
spreading of pollutants in mixing systems.