Regarding your new formulated question "my question boils down to whether a device similar to a voltmeter or thermometer exists for entropy":
Well in that case then the answer is no, you can only measure entropy by studying the change of its dependencies on extensive/intensive variables that influence it (as they are different in different systems). To make more contrast, take the example of liquid crystals, where one has to define an appropriate order parameter to study and to be able to quantify the entropy change of the system. (e.g. nematic order parameter, density, etc.)