The Gibbs–Boltzmann entropy effectively characterizes systems with a significant reliance on initial conditions. Nonetheless, the majority of materials generally exhibit behavior that is independent of their initial conditions. Conversely, Tsallis entropy—a nonextensive entropy that underpins nonextensive statistical mechanics—provides a comprehensive framework for modeling systems that engage with their environment. In this study, we derive the Tsallis formulation of the Clausius inequality in a quantum context and establish an upper limit for the work that can be extracted from a small system within the framework of nonextensive quantum statistical mechanics. Furthermore, by utilizing a principle from quantum information theory— which posits that erasing a single bit of information corresponds to the dissipation of a specific quantity of energy into the environment—we formulate an inequality for the erasure process in nonextensive systems. This principle aligns with the physical law that entropy can be transformed into heat. Additionally, we derive mutual information and integrate quantum feedback control to enhance Maxwell’s demon. Ultimately, we extend the second law of thermodynamics to information processes through the application of Tsallis entropy.
