Tomasz Kopczewski, University of Warsaw, Poland
Jan Lisicki, University of Warsaw, Poland
Tomasz Potocki, University of Rzeszow, Poland

Abstract: This paper introduces Entropy Lab, a decision-making instrument that began as a pedagogical device to make conditional entropy experiential and evolved into a research tool. Participants encounter four Markov-chain markets, each of which moves among three states. Across forty rounds, before investing in one market, they may purchase, at a fixed cost, a forecast of any market's next state. The markets share the same stationary distribution but differ in conditional entropy, making temporal predictability — how much today's state reveals about tomorrow's — measurable, priceable, allocable, and disruptable. The design integrates five literatures: Shannon information theory, Maxwell's demon and the thermodynamics of information, rational inattention, ergodic economics, and nonlinear-dynamical approaches to structural change. Its contribution lies in operationalising these perspectives within a single experimental task. At the midpoint, a hidden shock rotates all transition structures, reversing their entropy ranking. The task is implemented under additive and multiplicative payoff regimes, which differ in ergodic properties. Monte Carlo simulations benchmark four agent types, while an exploratory pilot indicates theoretically coherent behavioural variation. The article is presented as a proof of concept rather than a hypothesis test. An interactive implementation is available at: https:// microeconomics.shinyapps.io/entropy_lab/.

Keywords: conditional entropy, temporal uncertainty, rational inattention, Maxwell's demon, ergodic economics, Keynesian uncertainty, Markov chains