Search results for "Second law of thermodynamics"
showing 7 items of 7 documents
On the divide between animate and inanimate
2015
Vitalism was abandoned already for a long time ago, yet the impression that animate beings differ in some fundamental way from inanimate objects continues to thrive. Here, we argue that scale free patterns, found throughout nature, present convincing evidence that this demarcation is only imaginary. Therefore, all systems ought to be regarded alike, i.e., all are consuming free energy in least time. This way evolutionary processes can be understood as a series of changes from one state to another, so that flows of energy themselves naturally select those ways and means, such as species and societies or gadgets and galaxies to consume free energy in the least time in quest of attaining therm…
Thermodynamics based on the principle of least abbreviated action: Entropy production in a network of coupled oscillators
2006
We present some novel thermodynamic ideas based on the Maupertuis principle. By considering Hamiltonians written in terms of appropriate action-angle variables we show that thermal states can be characterized by the action variables and by their evolution in time when the system is nonintegrable. We propose dynamical definitions for the equilibrium temperature and entropy as well as an expression for the nonequilibrium entropy valid for isolated systems with many degrees of freedom. This entropy is shown to increase in the relaxation to equilibrium of macroscopic systems with short-range interactions, which constitutes a dynamical justification of the Second Law of Thermodynamics. Several e…
Systematic derivation of hydrodynamic equations for viscoelastic phase separation
2021
(abridged) We present a detailed derivation of a simple hydrodynamic two-fluid model, which aims at the description of the phase separation of non-entangled polymer solutions, where viscoelastic effects play a role. It is directly based upon the coarse-graining of a well-defined molecular model, such that all degrees of freedom have a clear and unambiguous molecular interpretation. The considerations are based upon a free-energy functional, and the dynamics is split into a conservative and a dissipative part, where the latter satisfies the Onsager relations and the Second Law of thermodynamics. The model is therefore fully consistent with both equilibrium and non-equilibrium thermodynamics.…
Substitution systems and nonextensive statistics
2015
Abstract Substitution systems evolve in time by generating sequences of symbols from a finite alphabet: At a certain iteration step, the existing symbols are systematically replaced by blocks of N k symbols also within the alphabet (with N k , a natural number, being the length of the k th block of the substitution). The dynamics of these systems leads naturally to fractals and self-similarity. By using B -calculus (Garcia-Morales, 2012) universal maps for deterministic substitution systems both of constant and non-constant length, are formulated in 1D. It is then shown how these systems can be put in direct correspondence with Tsallis entropy. A ‘Second Law of Thermodynamics’ is also prove…
Answering Schrödinger's "What Is Life?"
2020
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Geometric Aspects of Thermodynamics
2016
This chapter deals with mathematical aspects of thermodynamics most of which will be seen to be primarily of geometrical nature. Starting with a short excursion to differentiable manifolds we summarize the properties of functions, of vector fields and of one-forms on thermodynamic manifolds. This summary centers on exterior forms over Euclidean spaces and the corresponding differential calculus. In particular, one-forms provide useful tools for the analysis of thermodynamics. A theorem by Caratheodory is developed which is closely related to the second law of thermodynamics. The chapter closes with a discussion of systems which depend on two variables and for which there is an interesting a…
Analysis of a viscoelastic phase separation model
2020
A new model for viscoelastic phase separation is proposed, based on a systematically derived conservative two-fluid model. Dissipative effects are included by phenomenological viscoelastic terms. By construction, the model is consistent with the second law of thermodynamics, and we study well-posedness of the model, i.e., existence of weak solutions, a weak-strong uniqueness principle, and stability with respect to perturbations, which are proven by means of relative energy estimates. A good qualitative agreement with mesoscopic simulations is observed in numerical tests.