Elements of statistical physics formalism were applied to mutagenic and carcinogenic processes associated with cellular DNA; these are lesion (damage) creation, mutation creation, and cellular neoplastic (cancer) transformation. The probabilities of all state changes were strictly related to potential barrier heights between energetic states of DNA molecules. Barriers can be modified when radiation adaptive response mechanisms are applied, which are associated with a radiobiological quantity called radiosensitivity. It was discussed that radiosensitivity is determined by the cell's response to radiation resulting in three potential dose-response scenarios: linear, threshold, or hormetic. The type of dose-response is of critical importance in the development of radiation protection standards and individual radiation risk assessment. It is shown that the different scenarios describe different limits of the same underlying phenomena and the cell can respond in a linear, threshold, or hormetic way regarding its radiosensitivity. Finally, the dissipative adaptation mechanism is discussed in the context of proliferating cancer cells.