  We study the Stochastic Thermodynamics of cell growth and division using a
theoretical framework based on branching processes with resetting. Cell
division may be split into two sub-processes: branching, by which a given cell
gives birth to an identical copy of itself, and resetting, by which some
properties of the daughter cells (such as their size or age) are reset to new
values following division. We derive the first and second laws of Stochastic
Thermodynamics for this process, and identify separate contributions due to
branching and resetting. We apply our framework to well-known models of cell
size control, such as the sizer, the timer, and the adder. We show that the
entropy production of resetting is negative and that of branching is positive
for these models in the regime of exponential growth of the colony. This
property suggests an analogy between our model for cell growth and division and
heat engines, and the introduction of a thermodynamic efficiency, which
quantifies the conversion of one form of entropy production to another.
