  In a recent perspective article, Horowitz and Gingrich discuss thermodynamic
uncertainty relations that have been derived using "stochastic thermodynamics",
a theory based on a hypothesis known as local detailed balance. The authors
examined the foundations of this theory in their "Box 1: A brief primer on
local detailed balance and stochastic thermodynamics", where a kinetic scheme
for transport of particles between two reservoirs is presented. Horowitz and
Gingrich arrive at a relationship between the probability to cycle through the
states in one order vs. the probability to cycle in the reverse order. This
relation bears on the extremely important question of what governs
directionality when a system is driven away from equilibrium by contact with
multiple reservoirs that are not in equilibrium with one another. In the
original version of their paper the relation given for this ratio was obviously
wrong and contrary to the second law of thermodynamics. Based on our private
communications and on the recent paper authored by my colleagues and myself,
Horowitz and Gingrich accepted the necessity of correcting the error in their
Box 1. Unfortunately, in making the correction, the authors introduced an
equally serious, if less transparent, mistake, and continue to base their
theory on the thermodynamically impossible idea that transitions are mediated
by only one of the two reservoirs. In this comment we illustrate how the
principle of microscopic reversibility reveals that the true origin of
directional cycling amongst a network of states is kinetic asymmetry. This
understanding is important in guiding synthesis of molecular machines and other
devices designed to exploit transport or catalysis to drive non-equilibrium
processes.
