"Nevertheless, these difficulties are not the main reason for denying the central role played by entropy in the problem of the arrow of time in cosmology: there is a conceptual argument for abandoning the traditional approach. Entropy, as defined by thermodynamics, is a phenomenological property: a given value of entropy is compatible with many different configurations of a system. The question is whether there is a more fundamental property of the universe which allows us to distinguish between both temporal senses. From our perspective, it is possible to address the problem of the arrow of time in cosmology in terms of the geometrical properties of the space-time, independently of thermodynamic arguments. In this sense, we follow Earman’s “Time Direction Heresy”, according to which the arrow of time, if it exists, is an intrinsic feature of space-time “which does not need and cannot be reduced to nontemporal
features” (Earman, 1974, p.20). In other words, the geometrical approach has conceptual priority over the entropic approach, since the geometrical properties of the universe are more basic than its thermodynamic properties: the definition of entropy and the calculation of the entropy curve for the whole universe are possible only if the space-time has certain definite geometrical features. Therefore, to insist on entropic considerations for distinguishing between both temporal senses on the cosmological level can only be the result of the reductionistic attitude and its attempt of reducing temporal relations to non-temporal relations between events."