Entropy and the Typicality of Universes

Abstract

The universal validity of the second law of thermodynamics is widely attributed to a finely tuned initial condition of the universe. This creates a problem: why is the universe atypical? We suggest that the problem is an artefact created by inappropriate transfer of the traditional concept of entropy to the whole universe. Use of what we call the relational $N$-body problem as a model indicates the need to employ two distinct entropy-type concepts to describe the universe. One, which we call entaxy, is novel. It is scale-invariant and decreases as the observable universe evolves. The other is the algebraic sum of the dimensionful entropies of branch systems (isolated subsystems of the universe). This conventional additive entropy increases. In our model, the decrease of entaxy is fundamental and makes possible the emergence of branch systems and their increasing entropy. We have previously shown that all solutions of our model divide into two halves at a unique `Janus point' of maximum disorder. This constitutes a common past for two futures each with its own gravitational arrow of time. We now show that these arrows are expressed through the formation of branch systems within which conventional entropy increases. On either side of the Janus point, this increase is in the same direction in every branch system. We also show that it is only possible to specify unbiased solution-determining data at the Janus point. Special properties of these `mid-point data' make it possible to develop a rational theory of the typicality of universes whose governing law, as in our model, dictates the presence of a Janus point in every solution. If our self-gravitating universe is governed by such a law, then the second law of thermodynamics is a necessary direct consequence of it and does not need any special initial condition.

32 pages including 11 figures + 8 pages appendices/reflist. Included references which were missing in v1

References in corpus (6)

• Identification of a gravitational arrow of time
• Spontaneous Inflation and the Origin of the Arrow of Time
• Measure and Probability in Cosmology
• A Shape Dynamics Tutorial
• Conformal Superspace: the configuration space of general relativity
• Minimal Coupling and Attractors

Cited by in corpus (12)

• CPT-Symmetric Universe
• Through the Big Bang
• Switching quantum reference frames in the N-body problem and the absence of global relational perspectives
• Is the Hypothesis About a Low Entropy Initial State of the Universe Necessary for Explaining the Arrow of Time?
• A New Action for Cosmology
• Herglotz Action for Homogeneous Cosmology
• Pure shape dynamics: General framework
• A Proposal for a Metaphysics of Self-Subsisting Structures. I. Classical Physics
• $\Psi$-Epistemic Quantum Cosmology?
• Investigating total collisions of the Newtonian N-body problem on shape space
• Janus Points and Arrows of Time
• Entropy and Cosmological Arrows of Time