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Molecular line emission is a powerful probe of the physical conditions ofastrophysical objects but can be complex to model, and it is often unclearwhich transitions would be the best targets for observers who wish to constraina given parameter. We therefore produce a list of molecular species for whichthe gas history can be ignored, removing a major modelling complexity. We thendetermine the best of these species to observe when attempting to constrainvarious physical parameters. To achieve this, we use a large set of chemicalmodels with different chemical histories to determine which species haveabundances at 1 MYr that are insensitive to the initial conditions. We then useradiative transfer modelling to produce the intensity of every transition ofthese molecules. We finally compute the mutual information between the physicalparameters and all transitions and transition ratios in order to rank theirusefulness in determining the value of a given parameter.  We find 48 species that are insensitive to the chemical history of the gas,23 of which have collisional data available. We produce a ranked list of allthe transitions and ratios of these species using their mutual information withvarious gas properties. We show mutual information is an adequate measure ofhow well a transition can constrain a physical parameter by recovering knownprobes and demonstrating that random forest regression models become moreaccurate predictors when high-scoring features are included. Therefore, thislist can be used to select target transitions for observations in order tomaximize knowledge about those physical parameters.

History-independent tracers: Forgetful molecular probes of the physical conditions of the dense interstellar medium