Counting distinct states in physical dynamics

Abstract

Maximum counts of distinct states define important physical quantities, the most famous being entropy. Here we show that energy, momentum and other basic quantities of mechanics are also maximum counts. This generalizes a property familiar in communication with classical waves: frequency-width equals maximum number of distinct values that can be sent, per unit time. Basic mechanical quantities are frequency-widths of wavefunction evolution, and similarly bound number of distinct states. Evolutions that achieve maximum distinctness are effectively discrete. These properties refine our understanding of uncertainty, measurement, classical mechanics, and relativity.

Generalised quantum speed limit for arbitrary time-continuous evolution

“…We would like to mention that previous studies have derived speed limits for stochastic evolution, to which our speed limits are not applicable [93,94]. In references [95][96][97], speed limits have been derived that do not involve time evolution. Furthermore, there has been a recent extension of the concept of speed limits beyond state evolution, see references [5,[98][99][100][101][102][103][104].…”