H-theorem in quantum physics

“Remarkable progress of quantum information theory (QIT) allowed to formulate mathematical theorems for conditions that data-transmitting or data-processing occurs with a non-negative entropy gain. However, relation of these results formulated in terms of entropy gain in quantum channels to temporal evolution of real physical systems is not thoroughly understood. Here we build on the mathematical formalism provided by QIT to formulate the quantum H-theorem in terms of physical observables.

G. B. Lesovik, A. V. Lebedev, I. A. Sadovskyy, M. V. Suslov & V. M. Vinokur, “H-theorem in Quantum Physics“, Scientific Reports 6, Article number: 32815 (2016).

Towards a Grand Unified Theory of Mathematics and Physics

Peter Woit, University of Columbia, ‘Towards a Grand Unified Theory of Mathematics and Physics’.

A paper which outlines some of the already established connections between number theory and physics, acknowledges that there are as yet no satisfactory explanations for these connections, and concludes it is an area which deserves much more attention.

Essentially, the theory of everything set out here on this site argues that a grand unified theory of mathematics and physics requires only that mathematicians and physicists drop their peculiar insistence that number theory is nothing more than an abstract human concept.

It should be uncontroversial to state that 1a+2a=3a is clearly, self-evidently, a law of physics.

What constraints there may be on how the mathematical complexity of a physical universe develops from first principles, is a matter for focused investigation.