Heat flow and noncommutative quantum mechanics in phase-space

Journal of Mathematical Physics, Volume 61, Issue 12, December 2020. The complete understanding of thermodynamic processes in quantum scales is paramount to develop theoretical models encompassing a broad class of phenomena as well as to design new technological devices in which quantum aspects can be useful in areas such as quantum information and quantum computation. Among several quantum effects, the phase-space noncommutativity, which arises due to a deformed Heisenberg–Weyl algebra, is of fundamental relevance in quantum systems where quantum signatures and high energy physics play important roles. In low energy physics, however, it may be relevant to address how a quantum deformed algebra could influence some general thermodynamic protocols, employing the well-known noncommutative quantum mechanics in phase-space. In this work, we investigate the heat flow of two interacting quantum systems in the perspective of noncommutativity phase-space effects and show that by controlling the new constants introduced in the quantum theory, the heat flow from the hot to the cold system may be enhanced, thus decreasing the time required to reach thermal equilibrium. We also give a brief discussion on the robustness of the second law of thermodynamics in the context of noncommutative quantum mechanics.