We consider the cluster of problems raised by the relation between the notionof time, gravitational theory, quantum theory and thermodynamics; inparticular, we address the problem of relating the "timelessness" of thehypothetical fundamental general covariant quantum field theory with the"evidence" of the flow of time. By using the algebraic formulation of quantumtheory, we propose a unifying perspective on these problems, based on thehypothesis that in a generally covariant quantum theory the physical time-flowis not a universal property of the mechanical theory, but rather it isdetermined by the thermodynamical state of the system ("thermal timehypothesis"). We implement this hypothesis by using a key structural propertyof von Neumann algebras: the Tomita-Takesaki theorem, which allows to derive atime-flow, namely a one-parameter group of automorphisms of the observablealgebra, from a generic thermal physical state. We study this time-flow, itsclassical limit, and we relate it to various characteristic theoretical facts,as the Unruh temperature and the Hawking radiation. We also point out theexistence of a state-independent notion of "time", given by the canonicalone-parameter subgroup of outer automorphisms provided by the CocycleRadon-Nikodym theorem.
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