The first law of thermodynamics restates the law of conservation of energy. It partitions the change in energy of a system into two pieces, heat and work. While there is no ambiguity to define heat and work in classical thermodynamics, their classification in the quantum regime is not that obvious. Thus, the first law of thermodynamics becomes problematic in the quantum regime. However, recent studies have shown if contribution of quantum coherence is considered to the change of internal energy of the system, the first law of thermodynamics can be extended to the quantum domain. Here we investigate the new version of first law of thermodynamics for some quantum transformations by using two-level atomic system under non-dissipative channel. In our work we achieve a novel result that quantum coherence can be transformed into heat, and the heat can dissipate into the environments.
