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A statistical, path-dependent framework to describe time-dependentmacroscopic theories using the Principle of Maximum Caliber is presented. Bymeans of this procedure, it is possible to infer predictive non-equilibriumstatistical mechanical models from a variational principle, provided that theadequate time-dependent constraints and the state of the system at somespecific times are given. The approach is exemplified by obtaining thedescription of a time-dependent Brownian particle from kinetic restrictions. Werelate the predictive nature of a model to the structure of the priordistribution that represents the state of knowledge about the system before thedynamical constraints are considered. Non-predictive models are shown to bepossible in the presented framework and as an example, retrodictive dynamicsare obtained from the same kinetic constraints.

Prediction and Retrodiction in Statistical Mechanics from the Principle of Maximum Caliber