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Physical records and emergence of information in the gravitationally dominated universe

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The second law of thermodynamics appears to be a universal law of physics. This universality suggests that entropy and with it information theory is part of the foundations of physics.
In this talk I take the opposite (probably more conservative) approach: I assume that the dynamics of relational degrees of freedom form the foundation of physics. Physical information is an emergent phenomenon. This approach has an interesting consequence: Typical (initial) data for a gravitationally dominated universe leads to the spontaneous emergence of a gravitational arrow of time for the universe as a whole. This primary gravitational arrow of time generates secondary thermodynamic arrows of time in sufficiently isolated subsystems of the universe, which coincide with the gravitational arrow of time. This coincidence explains the universality of the second law of thermodynamics.
I conclude the talk with a speculation about the emergence of quantum information: I assume (1) that the purpose of a physical law is the prediction of future properties of the universe based on the knowledge of records and (2) that gravity generates physical records (as in the classical part of the talk). This suggests a scenario in which stable quantum information is spontaneously generated.
Collaborators for the classical part of the talk where Julian Barbour and Flavio Mercati