The fourth law of thermodynamics: steepest entropy ascent

Abstract

<jats:p>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 modelling the essential features of non-equilibrium 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 ‘fourth law of thermodynamics’. We state it as follows: every non-equilibrium 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-non-equilibrium realm within the framework of the rate-controlled constrained-equilibrium approximation (also known as the quasi-equilibrium approximation).</jats:p> <jats:p>This article is part of the theme issue ‘Fundamental aspects of nonequilibrium thermodynamics’.</jats:p>

Variational principles and nonequilibrium thermodynamics

“…Any methods that construct evolution equations with thermodynamic methods are contributing. We have already mentioned extended thermodynamics, GENERIC, conservation-dissipation formalism, steepest entropy descent, virtual power and internal variables [21,22,35,36,[68][69][70][71]. It is very successful in classical, non-relativistic situations where dissipation is apparent.…”

Nonequilibrium thermodynamics: emergent and fundamental

“…The third benchmark, backward compatibility, should precede the mathematical structure. The compatibility with a statistical treatment, based on a given microscopic or mesoscopic material composition, is a clear benchmark of any general phenomenology and appears here in the papers [1,10,12]. In particular, the compatibility with the kinetic theory is important in [8,6,7,3].…”

Quantum thermodynamics and quantum coherence engines

“…It is established by the Nernst theorem that sets vanishing entropy change in the limit of zero temperature [145,146]. Several works focus on placing the third law to quantum thermodynamics perspective [147][148][149][150][151][152]. Currently, the number of studies of the quantum version of the third law is relatively low.…”