  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.
