Abstract

The Boltzmann distribution encodes our subjective knowledge of the configuration in a classical lattice model, given only its Hamiltonian. If we acquire further information about the configuration from local measurements, then our knowledge is updated according to Bayes' theorem. I will argue that the resulting statistical ensembles (conditioned on measurements) show interesting new phase transitions. After discussing the interpretation of such transitions I will describe examples involving measurement of critical Ising and Potts models, of free fields, or of classical stochastic processes. I will comment on connections with constrained thermodynamic ensembles and with quantum problems and will note some open questions.