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2019

The information in a wave

Ciolli, Fabio, Longo, Roberto, Ruzzi, Giuseppe

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We provide the notion of entropy for a classical Klein-Gordon real wave, that we derive as particular case of a notion entropy for a vector in a Hilbert space with respect to a real linear subspace.

We then consider a localised automorphism on the Rindler spacetime, in the context of a free neutral Quantum Field Theory, that is associated with a second quantised wave, and we explicitly compute its entropy $S$, that turns out to be given by the entropy of the associated classical wave.
Here $S$ is defined as the relative entropy between the Rindler vacuum state and the corresponding sector state (coherent state).
By $\lambda$-translating the Rindler spacetime into itself along the upper null horizon, we study the behaviour of the corresponding entropy $S(\lambda)$.

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