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Progress in experimental techniques at nanoscale made measurements of noisein molecular junctions possible. These data are important source of informationnot accessible through average flux measurements. Emergence of optoelectronics,recently shown possibility of strong light-matter couplings, and developmentsin the field of quantum thermodynamics are making counting statisticsmeasurements of even higher importance. Theoretical methods for noiseevaluation in first principles simulations can be roughly divided intoapproaches applicable in the case of weak intra-system interactions, and thosetreating strong interactions for systems weakly coupled to baths. We argue thatdue to structure of its diagrammatic expansion and the fact of utilizingmany-body states as a basis of its formulation recently introducednonequilibrium Hubbard Green functions formulation is a relatively inexpensivemethod suitable for evaluation of noise characteristics in first principlessimulations over wide range of parameters. We illustrate viability of theapproach by simulations of noise and noise spectrum within generic models fornon-, weakly and strongly interacting systems. Results of the simulations arecompared to exact data (where available) and to simulations performed withinapproaches best suited for each of the three parameter regimes.

Towards Noise Simulation in Interacting Nonequilibrium Systems Strongly Coupled to Baths