Thermodynamics of fluid turbulence: a unified approach to the maximum transport properties

Onset model of mutually catalytic self-replicative systems formed by an assembly of polynucleotides

Self-replicability is a unique attribute observed in all living organisms, and the question of how the life was physically initiated could be equivalent to the question of how self-replicating informative polymers were formed in the abiotic material world. It has been suggested that the present DNA and proteins world was preceded by an RNA world in which genetic information of RNA molecules was replicated by the mutual catalytic function of RNA molecules. However, the important question of how the transition occurred from a material world to the very early pre-RNA world remains unsolved both experimentally and theoretically. We present an onset model of mutually catalytic self-replicative systems formed in an assembly of polynucleotides. A quantitative expression of the critical condition for the onset of growing fluctuation towards self-replication in this model is obtained by analytical and numerical calculations.

Convective flow in the presence of a small obstacle: Symmetry breaking, attractors, hysteresis, and information

This work explores the stability and hysteresis effects that occur when a small sink of momentum is introduced into a heat-driven, two-dimensional convective flow. As per standard fluid mechanical intuition, the system minimizes work generation and dissipation when one component of momentum is extracted. However, when the sink absorbs all incoming momentum, the system configures itself such that one of the convection plumes aligns directly with the sink. This state is the most hydrodynamically stable, but it maximizes, rather than minimizes extracted mechanical work. Furthermore, in the case of only vertical momentum extraction, there are two attractors, with different stabilities. Numerical experiments involving slow variations of the horizontal momentum extraction show a clear history dependence. This hysteresis preserves information about the system's past states, and hence represents a primitive memory. The momentum sink can also be used to manipulate the horizontal position of the flow field, with potential applications in microfluidics and laminar convection systems. This simple system exhibits the phenomena of autocatalysis (during the initial growth of the convection plumes), negative feedback (the attractors are either fully or quasistable), memory, and elementary computation.

Self-assembling outside equilibrium: emergence of structures mediated by dissipation

Self-assembly under non-equilibrium conditions may give rise to the formation of structures not available at equilibrium.

Living microorganisms change the information (Shannon) content of a geophysical system

The detection of microbial colonization in geophysical systems is becoming of interest in various disciplines of Earth and planetary sciences, including microbial ecology, biogeochemistry, geomicrobiology, and astrobiology. Microorganisms are often observed to colonize mineral surfaces, modify the reactivity of minerals either through the attachment of their own biomass or the glueing of mineral particles with their mucilaginous metabolites, and alter both the physical and chemical components of a geophysical system. Here, we hypothesise that microorganisms engineer their habitat, causing a substantial change to the information content embedded in geophysical measures (e.g., particle size and space-filling capacity). After proving this hypothesis, we introduce and test a systematic method that exploits this change in information content to detect microbial colonization in geophysical systems. Effectiveness and robustness of this method are tested using a mineral sediment suspension as a model geophysical system; tests are carried out against 105 experiments conducted with different suspension types (i.e., pure mineral and microbially-colonized) subject to different abiotic conditions, including various nutrient and mineral concentrations, and different background entropy production rates. Results reveal that this method can systematically detect microbial colonization with less than 10% error in geophysical systems with low-entropy background production rate.

Natural convection of a two-dimensional Boussinesq fluid does not maximize entropy production

Rayleigh-Bénard convection is a canonical example of spontaneous pattern formation in a nonequilibrium system. It has been the subject of considerable theoretical and experimental study, primarily for systems with constant (temperature or heat flux) boundary conditions. In this investigation, we have explored the behavior of a convecting fluid system with negative feedback boundary conditions. At the upper and lower system boundaries, the inward heat flux is defined such that it is a decreasing function of the boundary temperature. Thus the system's heat transport is not constrained in the same manner that it is in the constant temperature or constant flux cases. It has been suggested that the entropy production rate (which has a characteristic peak at intermediate heat flux values) might apply as a selection rule for such a system. In this work, we demonstrate with Lattice Boltzmann simulations that entropy production maximization does not dictate the steady state of this system, despite its success in other, somewhat similar scenarios. Instead, we will show that the same scaling law of dimensionless variables found for constant boundary conditions also applies to this system.

How does the Earth system generate and maintain thermodynamic disequilibrium and what does it imply for the future of the planet?

The Earth's chemical composition far from chemical equilibrium is unique in our Solar System, and this uniqueness has been attributed to the presence of widespread life on the planet. Here, I show how this notion can be quantified using non-equilibrium thermodynamics. Generating and maintaining disequilibrium in a thermodynamic variable requires the extraction of power from another thermodynamic gradient, and the second law of thermodynamics imposes fundamental limits on how much power can be extracted. With this approach and associated limits, I show that the ability of abiotic processes to generate geochemical free energy that can be used to transform the surface-atmosphere environment is strongly limited to less than 1 TW. Photosynthetic life generates more than 200 TW by performing photochemistry, thereby substantiating the notion that a geochemical composition far from equilibrium can be a sign for strong biotic activity. Present-day free energy consumption by human activity in the form of industrial activity and human appropriated net primary productivity is of the order of 50 TW and therefore constitutes a considerable term in the free energy budget of the planet. When aiming to predict the future of the planet, we first note that since global changes are closely related to this consumption of free energy, and the demands for free energy by human activity are anticipated to increase substantially in the future, the central question in the context of predicting future global change is then how human free energy demands can increase sustainably without negatively impacting the ability of the Earth system to generate free energy. This question could be evaluated with climate models, and the potential deficiencies in these models to adequately represent the thermodynamics of the Earth system are discussed. Then, I illustrate the implications of this thermodynamic perspective by discussing the forms of renewable energy and planetary engineering that would enhance the overall free energy generation and, thereby 'empower' the future of the planet.

Entropy production rate in a flux-driven self-organizing system

Entropy production rate (EPR) is often effective to describe how a structure is self-organized in a nonequilibrium thermodynamic system. The "minimum EPR principle" is widely applicable to characterizing self-organized structures, but is sometimes disproved by observations of "maximum EPR states." Here we delineate a dual relation between the minimum and maximum principles; the mathematical representation of the duality is given by a Legendre transformation. For explicit formulation, we consider heat transport in the boundary layer of fusion plasma [Z. Yoshida and S. M. Mahajan, Phys. Plasmas 15, 032307 (2008)]. The mechanism of bifurcation and hysteresis (which are the determining characteristics of the so-called H-mode, a self-organized state of reduced thermal conduction) is explained by multiple tangent lines to a pleated graph of an appropriate thermodynamic potential. In the nonlinear regime, we have to generalize Onsager's dissipation function. The generalized function is no longer equivalent to EPR; then EPR ceases to be the determinant of the operating point, and may take either minimum or maximum values depending on how the system is driven.

Minimization of a free-energy-like potential for non-equilibrium flow systems at steady state

This study examines a new formulation of non-equilibrium thermodynamics, which gives a conditional derivation of the 'maximum entropy production' (MEP) principle for flow and/or chemical reaction systems at steady state. The analysis uses a dimensionless potential function (st) for non-equilibrium systems, analogous to the free energy concept of equilibrium thermodynamics. Spontaneous reductions in (st) arise from increases in the 'flux entropy' of the system--a measure of the variability of the fluxes--or in the local entropy production; conditionally, depending on the behaviour of the flux entropy, the formulation reduces to the MEP principle. The inferred steady state is also shown to exhibit high variability in its instantaneous fluxes and rates, consistent with the observed behaviour of turbulent fluid flow, heat convection and biological systems; one consequence is the coexistence of energy producers and consumers in ecological systems. The different paths for attaining steady state are also classified.

Maximum or minimum entropy production? How to select a necessary criterion of stability for a dissipative fluid or plasma

Ten necessary criteria for stability of various dissipative fluids and plasmas are derived from the first and the second principle of thermodynamics applied to a generic small mass element of the system, under the assumption that local thermodynamic equilibrium holds everywhere at all times. We investigate the stability of steady states of a mixture of different chemical species at the same temperature against volume-preserving perturbations. We neglect both electric and magnetic polarization, and assume negligible net mass sources and particle diffusion. We assume that both conduction- and radiation-induced heat losses increase with increasing temperature. We invoke no Onsager symmetry, no detailed model of heat transport and production, no "Extended Thermodynamics," no "Maxent" method, and no "new" universal criterion of stability for steady states of systems with dissipation. Each criterion takes the form of--or is a consequence of--a variational principle. We retrieve maximization of entropy for isolated systems at thermodynamic equilibrium, as expected. If the boundary conditions keep the relaxed state far from thermodynamic equilibrium, the stability criterion we retrieve depends also on the detailed balance of momentum of a small mass element. This balance may include the nablap-related force, the Lorenz force of electromagnetism and the forces which are gradients of potentials. In order to be stable, the solution of the steady-state equations of motion for a given problem should satisfy the relevant stability criterion. Retrieved criteria include (among others) Taylor's minimization of magnetic energy with the constraint of given magnetic helicity in relaxed, turbulent plasmas, Rayleigh's criterion of stability in thermoacoustics, Paltridge 's maximum entropy production principle for Earth's atmosphere, Chandrasekhar' minimization of the adverse temperature gradient in Bénard's convective cells, and Malkus' maximization of viscous power with the constraint of given mean velocity for turbulent shear flow in channels. It turns out that characterization of systems far from equilibrium, e.g., by maximum entropy production is not a general property but--just like minimum entropy production--is reserved to special systems. A taxonomy of stability criteria is derived, which clarifies what is to be minimized, what is to be maximized and with which constraint for each problem.

Steady state of a dissipative flow-controlled system and the maximum entropy production principle

A theory to predict the steady-state position of a dissipative flow-controlled system, as defined by a control volume, is developed based on the maximum entropy principle of Jaynes, involving minimization of a generalized free-energy-like potential. The analysis provides a theoretical justification of a local, conditional form of the maximum entropy production principle, which successfully predicts the observable properties of many such systems. The analysis reveals a very different manifestation of the second law of thermodynamics in steady-state flow systems, which provides a driving force for the formation of complex systems, including life.

Variational formulation of nonequilibrium thermodynamics for hydrodynamic pattern formations

It is shown that a direct extension of the variational principle of near-equilibrium states due to Onsager leads to the analogous principle in hydrodynamic flows; the entropy production rate of an isolated system is maximized both near and far from equilibrium. It possesses as its extremal paths the solutions to the hydrodynamic equation of motion, and provides a general pattern selection criterion far from equilibrium.

The consequence of maximum thermodynamic efficiency in Daisyworld

The imaginary planet of Daisyworld is the simplest model used to illustrate the implications of the Gaia hypothesis. The dynamics of daisies and their radiative interaction with the environment are described by fundamental equations of population ecology theory and physics. The parameterization of the turbulent energy flux between areas of different biological cover is similar to the diffusive-type approximation used in simple climate models. Here I show that the small variation of the planetary diffusivity adopted in the classical version of Daisyworld limits the range of values for the solar insolation for which biota may grow in the planet. Recent studies suggest that heat transport in a turbulent medium is constrained to maximize its efficiency. This condition is almost equivalent to maximizing the rate of entropy production due to non-radiative sources. Here, I apply the maximum entropy principle (MEP) to Daisyworld. I conclude that the MEP sets the maximum range of values for the solar insolation with a non-zero amount of daisies. Outside this range, daisies cannot grow in the planet for any physically realistic climate distribution. Inside this range, I assume a distribution of daisies in agreement with the MEP. The results substantially enlarge the range of climate stability, due to the biota, in comparison to the classical version of Daisyworld. A very stable temperature is found when two different species grow in the planet.