Thermodynamics and Its Concepts in Nonequilibrium

Very recently, a new concept of time-reversed entropy per unit time was introduced as the complement of the Kolmogorov-Sinai entropy per unit time in order to make the connection with nonequilibrium thermodynamics and its entropy production [3]. This connection shows that the origin of entropy production can be... 

In this chapter, we will mainly consider the Gibbsian thermodynamics of phase equilibria relevant to problems in hydrocarbon reservoirs and use its concepts in the other chapters to solve practical problems. The thermodynamics of equilibrium processes also provide the framework for nonequilibrium and irreversible thermodynamics. It is our intention that the material covered in this book should be self-contained. The postulational approach introduced by Callen (1985), and Tisza (1966) is, therefore, adopted to make brief the presentation of basic concepts and equations. 

Of course, depending on the system, the optimum state identified by the second entropy may be the state with zero net transitions, which is just the equilibrium state. So in this sense the nonequilibrium Second Law encompasses Clausius Second Law. The real novelty of the nonequilibrium Second Law is not so much that it deals with the steady state but rather that it invokes the speed of time quantitatively. In this sense it is not restricted to steady-state problems, but can in principle be formulated to include transient and harmonic effects, where the thermodynamic or mechanical driving forces change with time. The concept of transitions in the present law is readily generalized to, for example, transitions between velocity macrostates, which would be called an acceleration, and spontaneous changes in such accelerations would be accompanied by an increase in the corresponding entropy. Even more generally it can be applied to a path of macrostates in time. 

The plan of this chapter is the following. Section II gives a summary of the phenomenology of irreversible processes and set up the stage for the results of nonequilibrium statistical mechanics to follow. In Section III, it is explained that time asymmetry is compatible with microreversibility. In Section IV, the concept of Pollicott-Ruelle resonance is presented and shown to break the time-reversal symmetry in the statistical description of the time evolution of nonequilibrium relaxation toward the state of thermodynamic equilibrium. This concept is applied in Section V to the construction of the hydrodynamic modes of diffusion at the microscopic level of description in the phase space of Newton s equations. This framework allows us to derive ab initio entropy production as shown in Section VI. In Section VII, the concept of Pollicott-Ruelle resonance is also used to obtain the different transport coefficients, as well as the rates of various kinetic processes in the framework of the escape-rate theory. The time asymmetry in the dynamical randomness of nonequilibrium systems and the fluctuation theorem for the currents are presented in Section VIII. Conclusions and perspectives in biology are discussed in Section IX. 

In Chapter 2, we pay a renewed visit to thermodynamics. We review its essentials and the common structure of its applications. In Chapter 3, we focus on so-called energy consumption and identify the concepts of work available and work lost. The last concept can be related to entropy production, which is the subject of Chapter 4. This chapter shows how some of the findings of nonequilibrium thermodynamics are invaluable for process analysis. Chapter 5 is devoted to finite-time finite-size thermodynamics, the application of which allows us to establish optimal conditions for operating a process with minimum losses in available work. 

This chapter starts with a simplified analysis of biological processes using the basic tools of physics, chemistry, and thermodynamics. It provides a brief description of mitochondria and energy transduction in the mitochondrion. The study of proper pathways and multi-inflection points in bioenergetics are summarized. We also summarize the concept of thermodynamic buffering caused by soluble enzymes and some important processes of bioenergetics using the linear nonequilibrium thermodynamics formulation. 

This section proposes first steps towards the evaluation and description of these multiphase systems and should help to stimulate a better understanding of them, which does not seem possible without the use of nonequilibrium thermodynamics. Further, it would be interesting, and I think it should be possible, to use the concepts that Eigen and Schuster [87] worked out for the complex problem of evolution —in combination with the ideas proposed by Ebeling [77c]—to come to a more basic description and a deeper understanding of multiphase systems. 

In this section we introduce these concepts in a very broad way, valid generally for any thermodynamics including nonequilibrium theories, to justify their application in our methodology. For this goal, only several primitives well-known from common life are sufficient. We use the SiUiavy s method [59, 60, 94-97], following mostly the papers of Kratochvfl and Silhavy [98, 99] (see Sects. 1.3, 1.4), because it is appropriate for (at least some) nonequilibrium situations. Unfortunately, this procedure has been demonstrated for pure materials only (for discussion of mixtures see below). 

With these concepts in hand, we may now briefly consider some thermodynamic aspects of solubility. Suppose (as above) one starts with pure solute (say, sodium chloride crystals) and pure solvent (water) and adds the salt crystals to the water at constant temperature. Just at the point when they are brought together, a nonequilibrium state exists, because salt has a finite solubility in water but has not yet dissolved. The concentration profile at this time is the step-function described in Fig. 1. The process of dissolving salt in water has a negative free energy, and thus occurs irreversibly until the liquid is saturated. As the concentration of salt in the liquid phase increases, so does its chemical potential, as seen from Eq. (4), and so the driving force for dissolution (the difference between the chemical potential at any given time and the equilibrium chemical potential) steadily decreases. Finally, a concentration is reached at which the chemical potential of sodium... 

The hierarchy that characterizes life is maintained through a multiplicity of catabolic and anabolic reactions, governed by a complex set of mechanisms that control the rate and timing of these processes. Thus, while this book will focus primarily on intermediary metabolism and its control mechanisms, in this chapter we will consider metabolic control from the viewpoint of nonlinear, nonequilibrium thermodynamics, which deals with the issue of how molecular events can be coupled and amplified so that they are expressed on a macroscopic level. The concepts herein expressed may be difficult to grasp at first reading. With perseverance, the beauty of the concepts will become apparent and their great importance for biological systems will become evident. 

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