  It is shown in the framework of a harmonic system that the thermodynamical
time arrow is induced by the environmental initial conditions in a manner
similar to spontaneous symmetry breaking. The Closed Time Path formalism is
introduced in classical mechanics to handle Green functions for initial
condition problems by the action principle, in a systematic manner. The
application of this scheme for quantum systems shows the common dynamical
origin of the thermodynamical and the quantum time arrows. It is furthermore
conjectured that the quantum-classical transition is strongly coupled.

Quantum Physics