Abstract
Entropy and the second law of thermodynamcs were discovered through study of the behaviour of gases in confined spaces. The related techniques developed in the kinetic theory of gases have failed to resolve the apparent conflict between the time-reversal symmetry of all known laws of nature and the existence of arrows of time that at all times and everywhere in the universe all point in the same direction. I will argue that the failure may be due to unconscious application to the universe of the conceptual framework developed for confined systems. If, as seems plausible, the universe is an unconfined system, new concepts are needed.
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Notes
- 1.
Fermi’s definition of the entropy [6] of out-of-equilibrium systems is illuminating. They must consist of subsystems each in equilibrium and separated by heat-insulating walls.
- 2.
This is also the most important condition required for Poincaré’s recurrence theorem to hold.
- 3.
Gibbs noted that this restriction has a counterpart in thermodynamics, in which “there is no thermodynamic equilibrium of a (finite) mass of gas in an infinite space”.
- 4.
That growth of the scale part of phase space must reduce the part corresponding to the remaining degrees of freedom was noted in connection with inflation in [8].
- 5.
- 6.
Planck’s well-known statement of the second law shows how essential it is to have complete control over the environment: “It is impossible to construct an engine which will work in a complete cycle and produce no effect except the raising of a weight and cooling of a heat reservoir.”
References
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Barbour, J. (2017). Arrows of Time in Unconfined Systems. In: Renner, R., Stupar, S. (eds) Time in Physics. Tutorials, Schools, and Workshops in the Mathematical Sciences . Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-68655-4_2
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DOI: https://doi.org/10.1007/978-3-319-68655-4_2
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