  When thermodynamics is understood as the science (or art) of constructing
effective models of natural phenomena by choosing a minimal level of
description capable of capturing the essential features of the physical reality
of interest, the scientific community has identified a set of general rules
that the model must incorporate if it aspires to be consistent with the body of
known experimental evidence. Some of these rules are believed to be so general
that we think of them as laws of Nature, such as the great conservation
principles, whose "greatness" derives from their generality, as masterfully
explained by Feynman in one of his legendary lectures. The second law of
thermodynamics is universally contemplated among the great laws of Nature. In
this paper we show that, in the past four decades, an enormous body of
scientific research devoted to modeling the essential features of
nonequilibrium natural phenomena has converged from many different directions
and frameworks towards the general recognition (albeit still expressed in
different but equivalent forms and language) that another rule is also
indispensable and reveals another great law of Nature that we propose to call
the \caporali{fourth law of thermodynamics}. We state it as follows: every
nonequilibrium state of a system or local subsystem for which entropy is
well-defined must be equipped with a metric in state space with respect to
which the irreversible component of its time evolution is in the direction of
steepest entropy ascent compatible with the conservation constraints. To
illustrate the power of the fourth law, we derive (nonlinear) extensions of
Onsager reciprocity and fluctuation-dissipation relations to the
far-nonequilibrium realm within the framework of the rate-controlled
constrained-equilibrium (RCCE) approximation (also known as the
quasi-equilibrium approximation).
