Algorithmic information and simplicity in statistical physics

Abstract

Given a list of $N$ states with probabilities $0<p_1\leq\cdots\leq p_N$, the average conditional algorithmic information $\bar I$ to specify one of these states obeys the inequality $H\leq\bar I<H+O(1)$, where $H=-\sum p_j\log_2p_j$ and $O(1)$ is a computer-dependent constant. We show how any universal computer can be slightly modified in such a way that the inequality becomes $H\leq\bar I<H+1$, thereby eliminating the computer-dependent constant from statistical physics.