Addendum to "Nonlinear quantum evolution with maximal entropy production"

The author calls attention to previous work with related results, which has escaped scrutiny before the publication of the article "Nonlinear quantum evolution with maximal entropy production", Phys.Rev.A63, 022105 (2001).Comment: RevTex-latex2e, 2pgs., no figs.; brief report to appear in the May 2001 issue of Phys.Rev.

Steepest-entropy-ascent irreversible relaxation towards thermodynamic equilibrium: the dynamical ansatz that completes the Gyftopoulos-Hatsopoulos unified theory with a general quantal law of causal evolution

<p>We overview the main features of the general equation of motion that completes the Gyftopoulos-Hatsopoulos unified theory of mechanics and thermodynamics with a quantal law of causal evolution that entails relaxation towards stable equilibrium for any non-equilibrium state, no matter how far from thermodynamic equilibrium. We illustrate with numerical examples the behavior of the equation of motion by discussing spontaneous energy redistribution within an isolated, closed system composed of non-interacting identical particles with energy levels ei and i = 1, 2,…, N. For this system the time-dependent occupation probabilities pi(t) obey the nonlinear rate equations which include functions of the pi(t)’s that maintain invariant the mean energy and the normalization condition. The entropy is a non-decreasing function of time until the initially nonzero occupation probabilities reach a Boltzmann-like canonical distribution over the occupied energy eigenstates. Initially zero occupation probabilities, instead, remain zero at all times. The solutions of the rate equations are unique and well-defined for arbitrary initial conditions pi(0) and for all times, -∞<t<+∞. Existence and uniqueness both forward and backward in time allows the reconstruction of the ancestral or primordial lowest entropy state. We also illustrate the structure and main properties of the nonlinear dynamics for a composite system.</p><ul><li>An initial version of this paper was published in<br />July of 2006 in the proceedings of ECOS’06, Aghia<br />Pelagia, Crete, Greece. </li></ul&gt

The Devil is in the details

Invited review of the book: R.J. Scully and M.O. Scully, The demon and the quantum, Wiley, 200

ENERGY AND ENTROPY BALANCES IN A COMBUSTION CHAMBER: ANALYTICAL SOLUTION.

An analytical solution of the energy and entropy balance equations for a combustible gas mixture contained in an open combustion chamber, for example of an internal combustion engine, is presented. The solution is free of major assumptions and is in a form suitable for incorporating any detailed models for the effects of wall heat transfer, wall thermal boundary layer, non-uniform temperature distributions in the burnt mixture, crevice regions, mass exchange through the boundaries of the chosen control volume and other similar effects. Explicit expressions for the instantaneous mass of burnt mixture and for the entropy generated by irreversibility are presented as functions of pressure and volume history of the combustion chamber and properties of the gas mixtures

Removing Heat and Conceptual Loops from the Definition of Entropy

A rigorous and general logical scheme is presented, which provides an operative non-statistical definition of entropy valid also in the nonequilibrium domain and free of the usual conceptual loops and unnecessary assumptions that restrict the traditional definition of entropy to the equilibrium domain. The scheme is based on carefully worded operative definitions for all the fundamental concepts employed, including those of system, state of a system, isolated system, separable system, systems uncorrelated form each other, environment of a system, process and reversible process. The treatment considers also systems with movable internal walls and/or semipermeable walls, with chemical reactions and and/or external force fields, and with small numbers of particles. The definition of entropy involves neither the concept of heat nor that of quasistatic process; it applies to both equilibrium and nonequilibrium states. Simple and rigorous proofs of the additivity of entropy and of the principle of entropy nondecrease complete the logical framework

Use of degree of disequilibrium analysis to select kinetic constraints for the rate-controlled constrained-equilibrium (RCCE) method

The Rate-Controlled Constrained-Equilibrium (RCCE) method provides a general framework that enables, with the same ease, reduced order kinetic modelling at three different levels of approximation: shifting equilibrium, frozen equilibrium, as well as non-equilibrium chemical kinetics. The method in general requires a significantly smaller number of differential equations than the dimension of the underlying Detailed Kinetic Model (DKM) for acceptable accuracies. To provide accurate approximations, however, the method requires accurate identification of the bottleneck kinetic mechanisms responsible for slowing down the relaxation of the state of the system towards local chemical equilibrium. In other words, the method requires that such bottleneck mechanisms be characterized by means of a set of representative constraints. So far, a drawback of the RCCE method has been the absence of a systematic algorithm that would allow a fully automatable identification of the best constraints for a given range of thermodynamic conditions and a required level of approximation. In this paper, we provide the first of two steps towards such algorithm based on the analysis of the degrees of disequilibrium (DoD) of chemical reactions in the underlying DKM. In any given DKM the number of rate-limiting kinetic bottlenecks is generally much smaller than the number of species in the model. As a result, the DoDs of all the chemical reactions effectively assemble into a small number of groups that bear the information of the rate-controlling constraints. The DoDs of all reactions in each group exhibit almost identical behaviour (time evolution, spatial dependence). Upon identification of these groups, the proposed kernel analysis of N matrices that are obtained from the stoichiometric coefficients yields the N constraints that effectively control the dynamics of the system. The method is demonstrated within the framework of modeling the expansion of products of the oxy-combustion of hydrogen through a quasi one-dimensional supersonic nozzle. The analysis predicts and RCCE simulations confirm that, under the geometrical and boundary conditions considered, the underlying DKM is accurately represented by only two bottleneck kinetic mechanisms, instead of the three constraints identified for the same problem in a recently published work also based, in part, on DoD analysis

Effects of climate change on the Nossana karst spring (northern Italy): future discharge projections and water distribution system sustainability

Nossana represents an important pre-Alpine karst spring located in Lombardy Region (Northern Italy). It is used for drinking supply and it sustains a water distribution system serving 300,000 people, including the city of Bergamo. The objective of this study was to project Nossana discharges, to evaluate potential supply limits for four future periods (2021-2040, 2041-2060, 2061-2080, 2081-2100). The study was carried out following a four-step approach. First, the EURO-CORDEX bias-corrected Regional Climate Models (RCMs) available for all the emission scenarios (RCP2.6, RCP4.5, RCP8.5) were evaluated in terms of precipitation and temperature monthly climatology. Second, they were statistically downscaled by means of change factors and a stochastic weather generator. Third, a rainfall-runoff model ensemble accounting also for snow dynamics (GR4J with CemaNeige module) was calibrated and validated on historical time series (1998-2017). Finally, the future downscaled time series were used as input in the calibrated model and the projected discharges evaluated in terms of low flow. In detail, two warning discharge thresholds - one for high water demand periods and one for ordinary water demand periods - were recognized with the service company managing the spring (Uniacque S.p.A.). Then, the number of (consecutive) days below them were calculated for each future period and compared to the historical time series. For each emission scenario, the calibrated model ensemble counted three RCMs and ten rainfall-runoff parameterizations. Projected ensemble mean discharges are lower than observations for all future periods and RCPs (from -3% for 2021-2040 and RCP4.5 to -23% for 2081-2100 and RCP8.5), although they do not show a clear trend between the four time periods. Days characterized by discharges lower than the warning thresholds are projected to decrease except for the RCP8.5 emission scenarios and the period 2081-2100 (14% increase for the ordinary-demand threshold, 10% increase for the high-demand threshold). Conversely, consecutive days are expected to increase between 2061 and 2100 for all emission scenarios and the two thresholds (by 0% and 26% for RCP 2.6, by 8% and 15% for RCP 4.5, by 28% and 48% for RCP 8.5). These results reflect the projected precipitation trend, characterized by longer, drier summer periods and wetter autumns in comparison to today\u2019s climate. Also, they indicate the need to develop a plan for the research and use of alternative drinking water resources for the long-term period. Therefore, the proposed methodology demonstrated to deliver useful information for water management planning. Future studies are intended to focus on chemistry and isotopic composition of water