Let's start out by removing the word hysteresis. The term is more so used in magnetism, motor core and transformer losses or in an event in the present compared to an event in the past. In so many words. Just so I can get a clearer meaning of things. What do you mean by hysteresis in the refrigeration world? Are you refering to the resistance to temperature change and the time needed to change the temperature of a given product? When trying to maintain a flat line product temperature or super close dead band, using the off the shelf electronic controller. You are basically, only controlling an event at the present time. The controller hasn't the electronic intelligence to do the hysteresis thing. It can't data process past events, like changing resperation rates/fermentation rates, compressor run time rates. The intelligence would be used to smooth out the run time of the condensor and lessen temp swing. The temp controller in a true chamber cycles a solenoid valve, or in the case of glycooled chamber, a modulating valve, not the compressor. There isn't a whole lot you can do to a domestic freezer, using a basic controller, that will eliminate beating up the compressor. Plus, a freezer compressor is designed to run at what is called a low back pressure. Also, the motor is cooled by low temp suction gas. Hence, frost on the suction line. Running the compressor in the 50 F range never allows the compressor to pull down to the low back pressure range, nor, will the motor be cooled adequately. The low back pressure is a result of the refrigerant boiling at close to -20. Less heat of rejection, the lower the pressure, the lower the running amps. The freezer is designed to have an initial pull down and then coast at 0 to -10. Running at constant 50 F, overloads the compressor. It has to reject too much heat. It doesn't matter if you put the sensor in the fermenter, tape it to the side or anything. The unit is still running in a high temp state. You'd be better off using a high temp cooler. Designed to run at 30 to 70F. Calling a domestic meat freezer a ferm chamber is like calling a haywagon an Indy racer. But, anyway. With the low cost of freezers today, so what if you burn a couple out. As long as you're making great beer. It's a small price to pay. I really appreciate the time you went through to produce the graph and your R & D endeavors. If you are dead set on using a freezer. You would be better off throwing a hundred or so feet of tubing on the bottom, load your families hamburger on top. Freeze the meat pops and circulate 0 F glycol through a jacketed fermenter or through a coil jammed in the fermentation bucket. Using a modulating thermostat, a 2 way modulating valve, and a circ pump. Kind of like the big boys do it.