Nonequilibrium Entropy Conservation and the Transport Equations of Mass, Momentum, and Energy

Nonequilibrium statistical mechanics or molecular theory has put the transport equations of mass, momentum and energy on a firm or rigorous theoretical foundation that has played a critical role in their use and applications. Here, it is shown that those methods can be extended to nonequilibrium entropy conservation. As already known, the “closure” of the transport equations leads to the theory underlying the phenomenological laws, including Fick’s Law of Diffusion, Newton’s Law of Viscosity, and Fourier’s Law of Heat. In the case of entropy, closure leads to the relationship of entropy flux to heat as well as the Second Law or the necessity of positive entropy generation. It is further demonstrated how the complete set of transport equations, including entropy, can be simplified under physically restrictive assumptions, such as reversible flows and local equilibrium flows. This analysis, in general, yields a complete, rigorous set of transport equations for use in applications. Finally, it is also shown how this basis set of transport equations can be transformed to a new set of nonequilibrium thermodynamic functions, such as the nonequilibrium Gibbs’ transport equation derived here, which may have additional practical utility.

Nonequilibrium Thermodynamics in Biochemical Systems and Its Application

Living systems are open systems, where the laws of nonequilibrium thermodynamics play the important role. Therefore, studying living systems from a nonequilibrium thermodynamic aspect is interesting and useful. In this review, we briefly introduce the history and current development of nonequilibrium thermodynamics, especially that in biochemical systems. We first introduce historically how people realized the importance to study biological systems in the thermodynamic point of view. We then introduce the development of stochastic thermodynamics, especially three landmarks: Jarzynski equality, Crooks’ fluctuation theorem and thermodynamic uncertainty relation. We also summarize the current theoretical framework for stochastic thermodynamics in biochemical reaction networks, especially the thermodynamic concepts and instruments at nonequilibrium steady state. Finally, we show two applications and research paradigms for thermodynamic study in biological systems.

La cultura biosófica garantista compleja como respuesta a la crisis ecológica y la construcción de la paz social

En este texto reflexionamos sobre la necesidad de cambiar nuestros hábitos y aprehender una nueva cultura garantista compleja que contribuya a restaurar la salud planetaria. Para lo cual es fundamental rebasar la ecología racionalista a través de los valores planteados por la biosofía desde el paradigma de la complejidad. Nuestro argumento central es que el paso de una sociedad disciplinaria y del rendimiento a una nueva sociedad −una sociedad del cansancio, en el sentido que le otorga Peter Handke−, requiere de una visión compleja que busque la generación de la paz territorial basada en la realidad político-social actual y que evite la autodestrucci.n del medio ambiente, del ser humano y por ende la paz. Palabras clave Biosofía, rendimiento, ecología, complejidad, garantismo Referencias Baudrillard, J. (1991). La transparencia del mal. Ensayos sobre fenómenos extremos, Anagrama, Barcelona. Bolaños Carmona, J. (2009). “Una Teoría de los Conflictos basada en la complejidad”, en Muñoz, Francisco A. y Molina Rueda, Beatriz (eds.). Una Paz compleja y conflictive, Universidad de Granada, Granada. Cano Pérez, M. Molina Rueda, B. y Francisco A. Muñoz. (2004). “Diálogos e Investigaciones Trans Culturales y Disciplinares”, en Convergencia, Año 11, Núm. 35, mayo-agosto, México. Handke, P. (2006). Ensayo sobre el cansancio, Alianza, Madrid. Heidegger, M. (2009), Ser y tiempo, Trotta, Madrid. Kay, J. (1991). “A nonequilibrium thermodynamic framework for discussing ecosystem integrity”, en Environmental Management, núm. 15. Latour B. (2012). Nunca fuimos modernos. Ensayos de antropología simétrica, Siglo XXI, Buenos Aires. Max-Neef, M. (1998). Desarrollo a escala humana. Conceptos, aplicaciones y algunas reflexiones, Icaria, Barcelona. Morin, E. (2006). El método V, Cátedra, Madrid. Nietzsche, F. (2011). Así hablo Zaratustra, Alianza, Madrid. Nietzsche, F. (2006). Humano, demasiado humano, Biblioteca Edaf, España.. Parker, David y Stacey, Ralph, “Chaos, Management, and Economics: The Implications of Non-Linear Thinking”, Institute for Economic Affairs; traducción al castellano en: “Caos, administración y economía. Las implicaciones de un pensamien-to no lineal”, Revista Libertas 24, Instituto Universitario ESEADE, 1996, Disponible en: http://www.eseade.edu.ar/servicios/Libertas/21_5_Parker%20y%20Stacey.pdf., Fecha de consulta: 20 de Agosto de 2019 Prigogine, I. (1997). El fin de las certidumbres, Taurus, Madrid. Sloterdijk, P. (2006). Normas para el parque humano,

Realization of the Landau definitions of effective Hamiltonian and nonequilibrium free energy in microscopic theory

Equilibrium fluctuations of some set of parameters in the states described by the canonical Gibbs distribution are investigated. In the theory of phase transitions of the second kind, these parameters are components of the order parameter. The microscopic realization of the Landau definition of the effective Hamiltonian of the system for studying the equilibrium fluctuations of the specified system of parameters is discussed in the terms of the probability density of their values. A general formula for this function is obtained and it is expressed through the equilibrium correlation functions of these parameters. An expression for the effective Hamiltonian in terms of deviations of the parameters from their equilibrium values is obtained. The deviations are considered small for conducting the calculations. The possibility of calculating the exact free energy of the system using the found effective Hamiltonian is discussed. In the microscopic theory, the implementation of the Landau definition of nonequilibrium thermodynamic potentials introduced in his phenomenological theory of phase transitions of the second kind is investigated. Nonequilibrium states of a fluctuating system described with some sets of parameters are considered. A general formula for nonequilibrium free energy expressed through the correlation functions of these parameters is obtained as for the effective Hamiltonian above. Like the previous case, the free energy expression via parameter deviations from the equilibrium values is obtained and small deviations are considered for calculations. The idea of the identity of the effective Hamiltonian of the system and its nonequilibrium free energy is discussed in connection with the Boltzmann distribution. The Gaussian approximation of both developed formalisms is considered. A generalization of the constructed theory for the case of spatially inhomogeneous states and the study of long-wave fluctuations are developed.

Nonlocal and nonlinear effects in hyperbolic heat transfer in a two-temperature model

The correct analysis of heat transport at nanoscale is one of the main reasons of new developments in physics and nonequilibrium thermodynamic theories beyond the classical Fourier law. In this paper, we provide a two-temperature model which allows to describe the different regimes which electrons and phonons can undergo in the heat transfer phenomenon. The physical admissibility of that model is showed in view of second law of thermodynamics. The above model is applied to study the propagation of heat waves in order to point out the special role played by nonlocal and nonlinear effects.