Mass conserved elementary kinetics is sufficient for the existence of a non-equilibrium steady state concentration

Living systems are forced away from thermodynamic equilibrium by exchange of mass and energy with their environment. In order to model a biochemical reaction network in a non-equilibrium state one requires a mathematical formulation to mimic this forcing. We provide a general formulation to force an arbitrary large kinetic model in a manner that is still consistent with the existence of a non-equilibrium steady state. We can guarantee the existence of a non-equilibrium steady state assuming only two conditions; that every reaction is mass balanced and that continuous kinetic reaction rate laws never lead to a negative molecule concentration. These conditions can be verified in polynomial time and are flexible enough to permit one to force a system away from equilibrium. In an expository biochemical example we show how a reversible, mass balanced perpetual reaction, with thermodynamically infeasible kinetic parameters, can be used to perpetually force a kinetic model of anaerobic glycolysis in a manner consistent with the existence of a steady state. Easily testable existence conditions are foundational for efforts to reliably compute non-equilibrium steady states in genome-scale biochemical kinetic models.Comment: 11 pages, 2 figures (v2 is now placed in proper context of the excellent 1962 paper by James Wei entitled "Axiomatic treatment of chemical reaction systems". In addition, section 4, on "Utility of steady state existence theorem" has been expanded.

The one-dimensional Stefan problem with non-Fourier heat conduction

We investigate the one-dimensional growth of a solid into a liquid bath, starting from a small crystal, using the Guyer-Krumhansl and Maxwell-Cattaneo models of heat conduction. By breaking the solidification process into the relevant time regimes we are able to reduce the problem to a system of two coupled ordinary differential equations describing the evolution of the solid-liquid interface and the heat flux. The reduced formulation is in good agreement with numerical simulations. In the case of silicon, differences between classical and non-classical solidification kinetics are relatively small, but larger deviations can be observed in the evolution in time of the heat flux through the growing solid. From this study we conclude that the heat flux provides more information about the presence of non-classical modes of heat transport during phase-change processes.Comment: 29 pages, 6 figures, 2 tables + Supplementary Materia

Thermodynamically consistent gradient elasticity with an internal variable

The role of thermodynamics in continuum mechanics and the derivation of the proper constitutive relations is a discussed subject of Rational Mechanics. The classical literature did not use the accumulated knowledge of thermostatics and was very critical with the heuristic methods of irreversible thermodynamics. In this paper, a small strain gradient elasticity theory is constructed with memory effects and dissipation. The method is nonequilibrium thermodynamics with internal variables; therefore, the constitutive relations are compatible with thermodynamics by construction. Thermostatic Gibbs relation is introduced for elastic bodies with a single tensorial internal variable. The thermodynamic potentials are first-order weakly nonlocal, and the entropy production is calculated. Then the constitutive functions and the evolution equation of the internal variable is constructed. The second law analysis has shown a contribution of gradient terms to the stress, also without dissipation.Comment: 17 pages, no figure

The origin of the spacetime metric: Bell's `Lorentzian pedagogy' and its significance in general relativity

The purpose of this paper is to evaluate the `Lorentzian pedagogy' defended by J.S. Bell in his essay ``How to teach special relativity'', and to explore its consistency with Einstein's thinking from 1905 to 1952. Some remarks are also made in this context on Weyl's philosophy of relativity and his 1918 gauge theory. Finally, it is argued that the Lorentzian pedagogy - which stresses the important connection between kinematics and dynamics - clarifies the role of rods and clocks in general relativity.Comment: To be published in ``Physics Meets Philosophy at the Planck Length'', C. Callender and N. Huggett (eds.), Cambridge University Press (1999). 22 pages, no figures, LaTeX, uses harvard.sty; 3 references added, typos corrected and minor changes to conten

Steepest Entropy Ascent Model for Far-Non-Equilibrium 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 non-equilibrium dynamics into a unified formulation, which extends to such frameworks the concept of Steepest Entropy Ascent (SEA) dynamics introduced by the present author in previous works on quantum thermodynamics. The present formulation constitutes a generalization also for the quantum thermodynamics framework. 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. In the near equilibrium limit, the metric tensor is related to the Onsager's generalized resistivity tensor. Therefore, through the identification of a suitable metric field which generalizes the Onsager generalized resistance to the arbitrarily far non-equilibrium domain, most of the existing theories of non-equilibrium thermodynamics can be cast in such a way that the state exhibits a spontaneous tendency to evolve in state space along the path of SEA compatible with the conservation constraints and the boundary conditions. The resulting unified family of SEA dynamical models is intrinsically and strongly consistent with the second law of thermodynamics. Non-negativity of the entropy production is a readily proved general feature of SEA dynamics. In several of the different approaches to non-equilibrium description we consider here, the SEA concept has not been investigated before. We believe it defines the precise meaning and the domain of general validity of the so-called Maximum Entropy Production Principle. It is hoped that the present unifying approach may prove useful in providing a fresh basis for effective, thermodynamically consistent, numerical models and theoretical treatments of irreversible conservative relaxation towards equilibrium from far non-equilibrium states.Comment: 15 pages, 4 figures, to appear in Physical Review

On the computation of moist-air specific thermal enthalpy

The specific thermal enthalpy of a moist-air parcel is defined analytically following a method in which specific moist entropy is derived from the Third Law of thermodynamics. Specific thermal enthalpy is computed by integrating specific heat content with respect to absolute temperature and including the impacts of various latent heats (i.e., solid condensation, sublimation, melting, and evaporation). It is assumed that thermal enthalpies can be set to zero at $0$ K for the solid form of the main chemically inactive components of the atmosphere (solid-$\alpha$ oxygen and nitrogen, hexagonal ice). The moist thermal enthalpy is compared to already existing formulations of moist static energy (MSE). It is shown that the differences between thermal enthalpy and the thermal part of MSE may be quite large. This prevents the use of MSE to evaluate the enthalpy budget of a moist atmosphere accurately, a situation that is particularly true when dry-air and cloud parcels mix because of entrainment/detrainment processes along the edges of cloud. Other differences are observed when MSE or moist-air thermal enthalpy is plotted on a psychrometric diagram or when vertical profiles of surface deficit are plotted.Comment: Paper accepted for publication (January 2014) in the Quarterly Journal of the Royal Meteorological Society (39 pages, 12 Figures, 7 Tables