Related papers: Thermodynamics and evolutionary biology through op…
We show that the equations which describe irreversible evolution of a system can be derived from a variational principle. We suggest a Lagrangian, which depends on the properties of the normal and the so-called "mirror-image" system. The…
The field-dependent equilibrium thermodynamics is derived with two methods: either by using the potential formalism either by the statistical method. Therefore, Pontrjagin's extremum principle of control theory is applied to an extended…
The population dynamics and stability of ecosystems of interacting species is studied from the perspective of non-equilibrium thermodynamics by assuming that species, through their biotic and abiotic interactions, are units of entropy…
Variational principles play a fundamental role in deriving evolution equations of physics. They are working well in case of nondissipative evolution but for dissipative systems they are not unique, not predictive and not constructive. With…
Life is a planetary feature that depends on its environment, but it has also strongly shaped the physical conditions on Earth, having created conditions highly suitable for a productive biosphere. Clearly, the second law of thermodynamics…
We outline a phenomenological theory of evolution and origin of life by combining the formalism of classical thermodynamics with a statistical description of learning. The maximum entropy principle constrained by the requirement for…
Thermodynamic relations are derived from first principles of mechanics for non-equilibrium processes. Since the key role herein is played by the law of increase of entropy, the latter is analyzed at first. It is shown that its derivation…
This paper aims to introduce a concept of an equilibrium point of a dynamical system which will call it almost global asymptotically stable. A biological prey-predator model is also analyzed with a modification function growth in prey…
The dynamics of molecular collisions in a macroscopic body are encoded by the parameter Thermodynamic entropy - a statistical measure of the number of molecular configurations that correspond to a given macrostate. Directionality in the…
Extremal principles are fundamental in our interpretation of phenomena in nature. One of the best known examples is the second law of thermodynamics, governing most physical and chemical systems and stating the continuous increase of…
Irreversible processes play a major role in the description and prediction of atmospheric dynamics. In this paper, we present a variational derivation of the evolution equations for a moist atmosphere with rain process and subject to the…
It is a common belief that in any environment where life is possible, life will be generated. Here it is suggested that the cause for a spontaneous generation of complex systems is probability driven processes. Based on equilibrium…
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…
A general nonequilibrium thermodynamic theory is developed for time-dependent Langevin dynamics, starting from the common definition of nonequilibrium Gibbs entropy. It is shown that the notations appearing in the First and the Second Law…
Motivated by infinite-dimensional optimal control problems with endpoint state constraints, in this Note, we introduce the notion of finite codimensional exact controllability for evolution equations. It is shown that this new…
The theory of evolution by natural selection cannot be used to evaluate the truth value of the following proposition: Through evolution, there exists at least one species that can adapt to any one given environment. To address this issue,…
The living organism is considered as an open system, whereas Prigogine's approach to the thermodynamics of such systems is used. The approach allows one to formulate the law of individual growth and development (ontogenesis) of the living…
For a class of stochastic delay evolution equations driven by cylindrical $Q$-Wiener process, we study the Pontryagin's maximum principle for the stochastic recursive optimal control problem. The delays are given as moving averages with…
Reciprocal relations correlate fairly accurately a great variety of experimental results. Nevertheless, the concepts of statistical fluctuations, and microscopic reversibility - the bases of the accepted proof of the relations by Onsager -…
The essential postulates of classical thermodynamics are formulated, from which the second law is deduced as the principle of increase of entropy in irreversible adiabatic processes that take one equilibrium state to another. The entropy…