  The rate of entropy production by a stochastic process quantifies how far it
is from thermodynamic equilibrium. Equivalently, entropy production captures
the degree to which detailed balance and time-reversal symmetry are broken.
Despite abundant references to entropy production in the literature and its
many applications in the study of non-equilibrium stochastic particle systems,
a comprehensive list of typical examples illustrating the fundamentals of
entropy production is lacking. Here, we present a brief, self-contained review
of entropy production and calculate it from first principles in a catalogue of
exactly solvable setups, encompassing both discrete- and continuous-state
Markov processes, as well as single- and multiple-particle systems. The
examples covered in this work provide a stepping stone for further studies on
entropy production of more complex systems, such as many-particle active
matter, as well as a benchmark for the development of alternative mathematical
formalisms.
