Seminar by Ralph Silva
ETH Zürich
The information theory of ticking clocks
Abstract
In this work we study a seemingly simple question relating physics and information theory: how many bits of information about time do we gain when we read off the value of a clock?
Our motivation for this question is as follows:
First, we would like to understand from a quantitative and operational point of view how much information a given clock provides about time, and we would like to be able to connect these considerations with basic quantities in physics, such as size, energy and thermodynamic resources.
Second, we expect that studying clocks from an information theoretic point of view will be beneficial in establishing general results characterizing the cost of communication of time-information in clock networks, in particular for tasks such as synchronization or accuracy-enhancement.
We propose a natural measure of time information based on a relative entropy between real clocks and "zero-information" clocks, and demonstrate that this measure relates naturally to existing quantifiers of accuracy and dynamical variables such as the size of the clock.