What does information cost? – On the price of an AI Chabot's work

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, 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.