AUTHOR=Asai Makoto , Cortés-Giraldo Miguel A. , Giménez-Alventosa Vicent , Giménez Gómez Vicent , Salvat Francesc TITLE=The PENELOPE Physics Models and Transport Mechanics. Implementation into Geant4 JOURNAL=Frontiers in Physics VOLUME=Volume 9 - 2021 YEAR=2021 URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2021.738735 DOI=10.3389/fphy.2021.738735 ISSN=2296-424X ABSTRACT=A translation of the {\sc penelope} physics subroutines to C++, designed as an extension of the Geant4 toolkit, is presented. The Fortran code system {\sc penelope} performs Monte Carlo simulation of coupled electron-photon transport in arbitrary materials for a wide energy range, nominally from 50 eV up to 1 GeV. {\sc penelope} implements the most reliable interaction models that are currently available, limited only by the required generality of the code. In addition, the transport of electrons and positrons is simulated by means of an elaborate class II scheme in which hard interactions (involving deflection angles or energy transfers larger than pre-defined cutoffs) are simulated from the associated restricted differential cross sections. After a brief description of the interaction models adopted for photons and electrons/positrons, we describe the details of the class-II algorithm used for tracking electrons and positrons. The C++ classes are adapted to the specific code structure of {\sc Geant4}. They provide a complete description of the interactions and transport mechanics of electrons/positrons and photons in arbitrary materials, which can be activated from the {\tt G4ProcessManager} to produce simulation results equivalent to those from the original {\sc penelope} programs. The combined code, named {\sc PenG4}, benefits from the multi-threading capabilities and advanced geometry and statistical tools of {\sc Geant4}.