The Arrow of Time and the Low-Entropy Past
Problem statement
The microscopic laws are (nearly) time-symmetric, yet entropy increases,
$$\frac{dS}{dt} \geq 0.$$
This macroscopic arrow is usually traced to an extraordinarily low-entropy initial state of the universe (the "Past Hypothesis").
Why did the early universe have such low entropy, and can the thermodynamic arrow be derived without simply postulating it?
Claims (1)
Partial result: under the additional assumption of a finite cutoff, one can show the bound holds. Full generality still open.
$$\|u(t)\|_{H^1} \leq C\,e^{\lambda t}$$
arXiv:2401.39519
Discussion (0)
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