The fourth law of thermodynamics: steepest entropy ascent.

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.

Time-Energy and Time-Entropy Uncertainty Relations in Nonequilibrium Quantum Thermodynamics under Steepest-Entropy-Ascent Nonlinear Master Equations.

In the domain of nondissipative unitary Hamiltonian dynamics, the well-known Mandelstam-Tamm-Messiah time-energy uncertainty relation τ F Δ H ≥ ℏ / 2 provides a general lower bound to the characteristic time τ F = Δ F / | d 〈 F 〉 / d t | with which the mean value of a generic quantum observable can change with respect to the width Δ F of its uncertainty distribution (square root of fluctuations). A useful practical consequence is that in unitary dynamics the states with longer lifetimes are those with smaller energy uncertainty Δ H (square root of energy fluctuations). Here we show that when unitary evolution is complemented with a steepest-entropy-ascent model of dissipation, the resulting nonlinear master equation entails that these lower bounds get modified and depend also on the entropy uncertainty Δ S (square root of entropy fluctuations).

Multi-physics interactions drive VEGFR2 relocation on endothelial cells.

Vascular Endothelial Growth Factor Receptor-2 (VEGFR2) is a pro-angiogenic receptor, expressed on endothelial cells (ECs). Although biochemical pathways that follow the VEGFR2 activation are well established, knowledge about the dynamics of receptors on the plasma membrane remains limited. Ligand stimulation induces the polarization of ECs and the relocation of VEGFR2, either in cell protrusions or in the basal aspect in cells plated on ligand-enriched extracellular matrix (ECM).

Essential equivalence of the general equation for the nonequilibrium reversible-irreversible coupling (GENERIC) and steepest-entropy-ascent models of dissipation for nonequilibrium thermodynamics.

By reformulating the steepest-entropy-ascent (SEA) dynamical model for nonequilibrium thermodynamics in the mathematical language of differential geometry, we compare it with the primitive formulation of the general equation for the nonequilibrium reversible-irreversible coupling (GENERIC) model and discuss the main technical differences of the two approaches. In both dynamical models the description of dissipation is of the "entropy-gradient" type. SEA focuses only on the dissipative, i.

Steepest entropy ascent model for far-nonequilibrium thermodynamics: unified implementation of the maximum entropy production principle.

By suitable reformulations, we cast the mathematical frameworks of several well-known different approaches to the description of nonequilibrium dynamics into a unified formulation valid in all these contexts, which extends to such frameworks the concept of steepest entropy ascent (SEA) dynamics introduced by the present author in previous works on quantum thermodynamics. Actually, the present formulation constitutes a generalization also for the quantum thermodynamics framework. The analysis emphasizes that in the SEA modeling principle a key role is played by the geometrical metric with respect to which to measure the length of a trajectory in state space.

Dissolution of a liquid microdroplet in a nonideal liquid-liquid mixture far from thermodynamic equilibrium.

A droplet placed in a liquid-liquid solution is expected to grow, or shrink, in time as approximately t;{1/2}. In this Letter, we report experimental evidence that when the composition in the interface is far from thermodynamic equilibrium due to the nonideality of the mixture, a droplet shrinks as approximately t. This scaling is due to the coupling between mass and momentum transfer known as Korteweg forces as a result of which the droplet self-propels around.

Nonlinear model dynamics for closed-system, constrained, maximal-entropy-generation relaxation by energy redistribution.

We discuss a nonlinear model for relaxation by energy redistribution within an isolated, closed system composed of noninteracting identical particles with energy levels with . The time-dependent occupation probabilities are assumed to obey the nonlinear rate equations where and are functionals of the 's that maintain invariant the mean energy and the normalization condition . The entropy is a nondecreasing function of time until the initially nonzero occupation probabilities reach a Boltzmann-like canonical distribution over the occupied energy eigenstates.

Thermodynamic derivations of conditions for chemical equilibrium and of Onsager reciprocal relations for chemical reactors.

For an isolated chemical reactor, we derive the conditions for chemical equilibrium in terms of either energy, volume, and amounts of constituents or temperature, pressure, and composition, with special emphasis on what is meant by temperature and chemical potentials as the system proceeds through nonequilibrium states towards stable chemical equilibrium. For nonequilibrium states, we give both analytical expressions and pictorial representations of the assumptions and implications underlying chemical dynamics models. In the vicinity of the chemical equilibrium state, we express the affinities of the chemical reactions, the reaction rates, and the rate of entropy generation as functions of the reaction coordinates and derive Onsager reciprocal relations without recourse to statistical fluctuations, time reversal, and the principle of microscopic reversibility.