  The evolution of the joint system (JS) - ``quantum system (QS)+thermal bath
(TB)" is considered in the framework of a complex probabilistic processes that
satisfies the stochastic differential equation of the Langevin-Schr\"{o}dinger
type. Two linearly coupled oscillators that randomly interact with the
environment and with each other are selected as QS. In the case when the
interactions obey the law of a white random process, all the construction of
the statistical parameters of the QS and its environment are performed
analytically in the form of double integrals and solutions of second-order
partial differential equations. Expressions of time-dependent von Neumann
entropy and its generalization are obtained, taking into account the
self-organization and entanglement processes occurring in the JS. It is
mathematically proved that as a result of the relaxation of JS in the TB, a
small quantized environment is formed, which can be interpreted as a
continuation of QS or its halo. Bell states formed as a result of the decay of
coupled two linear oscillators are constructed taking into account the
influence of the environment. The transitions between $(in)$ and $(out$)
asymptotic states of QS are studied in detail taking into account the influence
of TB. Within the framework of the model problem, the possibility of
constructing quantum thermodynamics from the first principle is proved without
using any additional conditions.
