Abstract This paper examines the information provided by an AI Chatbot. The starting point is Shannon’s technical concept of information, which treats the message y ∈ 𝒴 as a formal selection from a set of possible responses 𝒴 to a prompt x ∈ 𝒳. The relevant statistical quantities are the conditional self-information i(y|x) and, on average, the conditional entropy H(Y|X = x), where X and Y denote the random variables of the prompt and the response. Landauer’s principle links information theory with thermodynamics; through the concept of entropy, it forms a bridge between information and energy in the form of a thermodynamic lower bound on heat for logically irreversible processes. This thermodynamic minimum energy is vanishingly small compared to the actual production energy Eprod(x,y) of the response y on the provider’s side, which in turn represents only one component of the production costs Kprod(x,y) alongside computing time, thinking time, storage, infrastructure and proportionate system costs. Using the example x = ‘Name a prime number less than 10’, the transition from the theoretical information value of a specific response y to a rough price estimate for an AI chat is illustrated.
Siegfried Weinmann (Thu,) studied this question.