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Time-arrow $s=+/-$, intrinsic to a concrete physical system, is associatedwith the direction of information loss $\Delta I$ displayed by the randomevolution of the given system. When the information loss tends to zero theintrinsic time-arrow becomes uncertain. We propose the heuristic relationship$1/[1+exp(-s\Delta I)]$ for the probability of the intrinsic time-arrow. Themain parts of the present work are trying to confirm this heuristic equation.The probability of intrinsic time arrow is defined by Bayesian inference fromthe observed random process. From irreversible thermodynamic systems, theproposed heuristic probabilities follow via the Gallavotti-Cohen relationsbetween time-reversed random processes. In order to explore the underlyingmicroscopic mechanism, a trivial microscopic process is analyzed and an obviousdiscrepancy is identified. It can be resolved by quantum theory. Thecorresponding trivial quantum process will exactly confirm the proposedheuristic time-arrow probability.Comment: 13pp, revtex4, to appear in Proceedings of DICE 2002 (Springer, LNP

Probability of Intrinsic Time-Arrow from Information Loss