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We present a new implementation of the tracer particles algorithm based on aMonte Carlo approach for the Eulerian adaptive mesh refinement code Ramses. Thepurpose of tracer particles is to keep track of where fluid elements originatein Eulerian mesh codes, so as to follow their Lagrangian trajectories andre-processing history. We provide a comparison to the more commonly usedvelocity-based tracer particles, and show that the Monte Carlo approachreproduces the gas distribution much more accurately. We present a detailedstatistical analysis of the properties of the distribution of tracer particlesin the gas and report that it follows a Poisson law. We extend these MonteCarlo gas tracer particles to tracer particles for the stars and black holes,so that they can exchange mass back and forth between themselves. With such ascheme, we can follow the full cycle of baryons, that is, from gas-formingstars to the release of mass back to the surrounding gas multiple times, oraccretion of gas onto black holes. The overall impact on computation time is$\sim$ 3% per tracer per initial cell. As a proof of concept, we study anastrophysical science case -- the dual accretion modes of galaxies at highredshifts --, which highlights how the scheme yields information hithertounavailable. These tracer particles will allow us to study complexastrophysical systems where both efficiency of shock-capturing Godunov schemesand a Lagrangian follow-up of the fluid are required simultaneously.

Accurate tracer particles of baryon dynamics in the adaptive mesh refinement code Ramses