This is a review of the problem of thermodynamical arrow of time, and includes often-discussed arguments and some comparatively recent papers whose claims are not mainstream. The mathematical instrument that describes the framework of the time's arrow problem is confirmed and the logical relation is formalized, where we distinguish time asymmetry and time noninvertibility. We review and critically investigate some papers that possibly can be conceptual foundations of the mathematical and logical relations. Especially, we focus on the following novel approaches: time symmetry of stochastic processes without considering constraint conditions and the law of entropy increase as explicans, i.e., what explains something.

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