Abstract
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.
Highlights
The fundamental equations of motions are time reversal invariant when weak interaction is ignored and the emergence of past and future, an orientation of time is an interesting, open question [1, 2, 3]
It is argued below that the thermodynamical time arrow, irreversibility, is generated by a spontaneous breakdown of time reversal invariance and has the same dynamical origin as decoherence, thereby the thermodynamical and quantum time arrows are identical. These points will be demonstrated in the framework of harmonic systems. To render this argument valid for weakly interactive systems one needs the Closed Time Path (CTP) formalism which will briefly be introduced in classical mechanics [4]
The CTP formalism is needed in quantum physics when the density matrix ρ(t) = U (t, 0)ρ(0)U †(t, 0) or expectation values, A (t) = Tr[Aρ(t)] are sought
Summary
The fundamental equations of motions are time reversal invariant when weak interaction is ignored and the emergence of past and future, an orientation of time is an interesting, open question [1, 2, 3]. It is argued below that the thermodynamical time arrow, irreversibility, is generated by a spontaneous breakdown of time reversal invariance and has the same dynamical origin as decoherence, thereby the thermodynamical and quantum time arrows are identical These points will be demonstrated in the framework of harmonic systems. A time arrow is set dynamically and the corresponding dynamics is irreversible if the time arrow is formed even before imposing the boundary conditions on time on the system coordinate This may happen if the environment time arrows, as external agents manage to break the time reversal invariance of the effective system dynamics. There are two ways to detect spontaneous symmetry breaking, a dynamical and a static procedure
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