Improved Landauer's principle and generalized second law of thermodynamics with initial correlations and non-equilibrium surrounding environments

Traditional form of the second law of thermodynamics is strongly restricted by three conditions: One is the initial joint state of the system and surroundings should be a product state, so that there exists no initial correlations. The second is the initial states of surroundings are in equilibrium thermodynamics. And the end is weak couplings between the system and surroundings. This formulation of the second law should be reexamined in order to understand the relations of thermodynamics and information theory, especially, when existing initial correlations. In this work, using the techniques of quantum statistical mechanics for thermodynamics and quantum information science, we recast fundamental laws of thermodynamics from theoretical information point of view. Initial correlations between the system and surroundings are considered, which evolves thermodynamically and result in modifications of the traditional formulations. We obtained improved forms of the entropy increase, Landauer's principle, and the second law of thermodynamics, which are exhibited as equalities rather than inequalities, and through which physical nature of information can be demonstrated precisely. Further, using the language totally belongs to quantum information theory, we give the direction of natural evolution process a new statement: the evolution of an isolated quantum system, where no correlations exist between subsystems, initially, always towards to directions of the correlation information never be decreased. Such result indicates that the traditional principle of entropy increase can be redescribed using information theory, identically.