Maximum entropy methods are at the core of a new view of scientific inference, allowing analysis and interpretation of large and sometimes noisy data. Surprisal analysis extends principles of maximal entropy and of thermodynamics, where both equilibrium thermodynamics and statistical mechanics are assumed to be inferential processes. This enables surprisal analysis to be an effective method of information quantification and compaction and of providing an unbiased characterization of systems. Surprisal analysis is particularly useful to characterize and understand dynamics in small systems, where energy fluxes that are otherwise negligible in large systems heavily influence system behavior.