Articles have appeared that rely on the application of some form of "maximum local entropy production principle" (MEPP). This is usually an optimization principle that is supposed to compensate for the lack of structural information and measurements about complex systems, even systems as complex and as little characterized as the whole biosphere or the atmosphere of the Earth or even of less known bodies in the solar system. We select a number of claims from a few well-known papers that advocate this principle and we show that they are in error with the help of simple examples of well-known chemical and physical systems. These erroneous interpretations can be attributed to ignoring well-established and verified theoretical results such as (1) entropy does not necessarily increase in nonisolated systems, such as "local" subsystems; (2) macroscopic systems, as described by classical physics, are in general intrinsically deterministic-there are no "choices" in their evolution to be selected by using supplementary principles; (3) macroscopic deterministic systems are predictable to the extent to which their state and structure is sufficiently well-known; usually they are not sufficiently known, and probabilistic methods need to be employed for their prediction; and (4) there is no causal relationship between the thermodynamic constraints and the kinetics of reaction systems. In conclusion, any predictions based on MEPP-like principles should not be considered scientifically founded.

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Calculating the probability of each possible outcome for a patient at any time in the future is currently possible only in the simplest cases: short-term prediction in acute diseases of otherwise healthy persons. This problem is to some extent analogous to predicting the concentrations of species in a reactor when knowing initial concentrations and after examining reaction rates at the individual molecule level. The existing theoretical framework behind predicting contagion and the immediate outcome of acute diseases in previously healthy individuals is largely analogous to deterministic kinetics of chemical systems consisting of one or a few reactions. We show that current statistical models commonly used in chronic disease epidemiology correspond to simple stochastic treatment of single reaction systems. The general problem corresponds to stochastic kinetics of complex reaction systems. We attempt to formulate epidemiologic problems related to chronic diseases in chemical kinetics terms. We review methods that may be adapted for use in epidemiology. We show that some reactions cannot fit into the mass-action law paradigm and solutions to these systems would frequently exhibit an antiportfolio effect. We provide a complete example application of stochastic kinetics modeling for a deductive meta-analysis of two papers on atrial fibrillation incidence, prevalence, and mortality.M uch of the medical progress over the last century can be attributed to the objective assessment of the effect of treatments on the evolution of specific diseases. Treatment effect is measured as the rate of an event such as recovery in a sample of the patient population. Relatively immediate results were obtained from studies involving acute diseases, occurring in previously healthy individuals, in which recovery could be clearly identified. This resulted in the development of effective treatments for most acute diseases affecting children and younger adults and a substantial prolongation of life expectancy (1). Consequently, many acute diseases were treated effectively. This led to the current, more complex situation, in which an elderly population suffers from a combination of chronic conditions. Few older people are strictly healthy, and besides the evolution of the chronic conditions themselves, acute diseases occurring in this setting do not always evolve as in a young, healthy population. This combination of chronic conditions and risk factors amounts to the presence of more heterogenous populations. Thus, samples need to be larger to allow reproducible predictions, compared with those for acute diseases occurring in a young and previously healthy population. Predictions that are also more complex (there is no strict "recovery") apply to a limited range of cases.The concepts used by clinicians and epidemiologists to describe the health status of individuals and their prevalence in the population, as well as the rates of change in this status and the general predictive laws, are quite analogous to the concepts used by chemists for p...

The Luo-Rudy I model, describing the electrophysiology of a ventricular cardiomyocyte, is associated with an 8-dimensional discontinuous dynamical system with logarithmic and exponential non-linearities depending on 15 parameters. The associated stationary problem was reduced to a nonlinear system in only two unknowns, the transmembrane potential V and the intracellular calcium concentration [Ca]( i ). By numerical approaches appropriate to bifurcation problems, sections in the static bifurcation diagram were determined. For a variable steady depolarizing or hyperpolarizing current (I (st)), the corresponding projection of the static bifurcation diagram in the (I (st), V) plane is complex, featuring three branches of stationary solutions joined by two limit points. On the upper branch oscillations can occur, being either damped at a stable focus or diverted to the lower branch of stable stationary solutions when reaching the unstable manifold of a homoclinic saddle, thus resulting in early after-depolarizations (EADs). The middle branch of solutions is a series of unstable saddle points, while the lower one a series of stable nodes. For variable slow inward and K(+) current maximal conductances (g (si) and g (K)), in a range between 0 and 4-fold normal values, the dynamics is even more complex, and in certain instances sustained oscillations tending to a limit cycle appear. All these types of behavior were correctly predicted by linear stability analysis and bifurcation theory methods, leading to identification of Hopf bifurcation points, limit points of cycles and period doubling bifurcations. In particular settings, e.g. one-fifth-of-normal g (si), EADs and sustained high amplitude oscillations due to an unstable resting state may occur simultaneously.

We introduce systematic approaches to chemical kinetics based on the use of phase-phase (log-log) representations of the rate equations. For slow processes, we obtain a corrected form of the mass-action law, where the concentrations are replaced by kinetic activities. For fast reactions, delay expressions are derived. The phase-phase expansion is, in general, applicable to kinetic and transport processes. A mechanism is introduced for the occurrence of a generalized mass-action law as a result of self-similar recycling. We show that our self-similar recycling model applied to prothrombin assays reproduces the empirical equations for the International Normalized Ratio calibration (INR), as well as the Watala, Golanski, and Kardas relation (WGK) for the dependence of the INR on the concentrations of coagulation factors. Conversely, the experimental calibration equation for the INR, combined with the experimental WGK relation, without the use of theoretical models, leads to a generalized mass-action type kinetic law.rate equations ͉ expansions ͉ prothrombin assays ͉ international normalized ratio