Everettian Formulation of the Second Law of Thermodynamics

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Abstract
The second law of thermodynamics is traditionally interpreted as a coarse-grained result of classical mechanics. Recently its relation with quantum mechanical processes such as decoherence and measurement has been revealed in literature. In this paper we will formulate the second law and the associated time irreversibility following Everett’s idea: systems entangled with an object getting to know the branch in which they live. Accounting for this self-locating knowledge, we get two forms of entropy: objective entropy measuring the uncertainty of the state of the object alone, and subjective entropy measuring the information carried by the self-locating knowledge. By showing that the summation of the two forms of entropy is a conserved and perspective-free quantity, we interpret the second law as a statement of irreversibility in knowledge acquisition. This essentially derives the thermodynamic arrow of time from the subjective arrow of time, and provides a unified explanation for varieties of the second law, as well as the past hypothesis.
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Archival date: 2021-09-01
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