Total Entropy Generation in Thermodynamics Formulas

Yes, the Total Entropy Generation, measured in Specific Entropy can be negative.

Total Entropy Generation is usually measured using the Joule per Kilogram K[J/kg*K] for Specific Entropy. Calorie per Gram per Celcius[J/kg*K], Joule per Kilogram per Celcius[J/kg*K], Kilojoule per Kilogram per Celcius[J/kg*K] are the few other units in which Total Entropy Generation can be measured.