<p>In water electrolysis, the formation of gas bubbles is a complex dissipative process, where entropy is produced irreversibly. The understanding of which is significant for all electrolyzer optimizations. To this end, we have introduced the information-entropy as a new variable into electrolysis research for the first time. An electrochemical cell was designed, where the evolution of hydrogen gas bubbles on a flat electrode surface could be observed through a glass window, using a high-speed camera and microscope objective. Within three experiments with different nickel electrodes, an innovative grey scale pixel analysis was applied to compute the information-entropy (Shannon-entropy), presenting the information content and disorder of multifaceted bubble evolution. With increasing current density, we observed a remarkable correlation between this information-entropy and the Gibbs entropy derived from the overvoltage. At high power levels, huge amounts of entropy and information are produced, measurable in the form of chaotic bubble evolution patterns. Large bubbles play a key role here - with complex multi-physical phenomena. Blocking of the electrode surface is more than compensated because of thin film diffusion. An innovative micro-region model presents significantly higher local entropy production at the 3-phase contact line. Soon, the entropy-information model will be used to develop highly efficient electrodes, nucleation sites, and flow structures for enhanced mass transport and minimized exergetic losses due to bubble formation.</p>