Thermodynamic systems dissipation

These patterns are an example of what are sometimes called dissipative structures, which arise in many complex systems. Dissipative structures are dynamical patterns that retain their organized state by persistently dissipating matter and energy into an otherwise thermodynamically open environment. 

G. Nicolis and I. Prigogine, Exploring Complexity, Piper, Munich, 1987 (a technical exposition of the thermodynamics of dissipative systems far from thermodynamic equilibrium). 

There exist a large number of phenomenological laws for example, Fick s law relates to the flow of a substance and its concentration gradient, and the mass action law explores the reaction rate and chemical concentrations or affinities. When two or more of these phenomena occur simultaneously in a system, they may couple and induce new effects, such as facilitated and active transport in biological systems. In active transport, a substrate can flow against the direction imposed by its thermodynamic force. Without the coupling, such uphill transport would be in violation of the second law of thermodynamics. Therefore, dissipation due to either diffusion or chemical reaction can be negative only if these two processes couple and produce a positive total entropy production. 

The equality of this equation represents a system at equilibrium where JT = A = 0. The work done by the controlling system dissipates as heat. This is in line with the first law of thermodynamics. The inequality in Eq. (11.4) represents the second law of thermodynamics. The cyclic chemical reaction in nonequilibrium steady-state conditions balances the work and heat in compliance with the first law and at the same time transforms useful energy into entropy in the surroundings in compliance with the second law. The dissipated heat related to affinity A under these conditions is different from the enthalpy difference AH° = (d(Aii°/T)/d(l/Tj). The enthalpy difference can be positive if the reaction is exothermic or negative if the reaction is endothermic. On the other hand, the A contains the additional energy dissipation associated with removing a P molecule from a solution with concentration cP and adding an S molecule into a solution with concentration cs. 

Now definitions or frameworks of modem thermodynamics in a broad sense, of classical thermodynamics, and of modem thermodynamics in a narrow sense are very clear. Modern thermodynamics in a broad sense includes all fields of thermodynamics (both classical thermodynamics and modem thermodynamics in a narrow sense) for any macroscopic system, but modem thermodynamics in a narrow sense includes only three fields of thermodynamics, i.e., nonequilibrium nondissipative thermodynamics, linear dissipative thermodynamics and nonlinear dissipative thermodynamics. The modem thermodynamics in a narrow sense should not be called nonequilibrium thermodynamics, because the classical nonequilibrium thermodynamics is not included. Meanwhile, the classical thermodynamics should only be applied to simpler systems without reaction coupling. That is, the application of classical thermodynamics to some modem inorganic syntheses and to the life science may be not suitable. Without the self-consistent classification of modem thermodynamics it was very difficult to really accept the term of modem thermodynamics even only for teaching courses. 

Keywords. Thermodynamics, Phase equilibria, Biotechnology, Biochemical engineering. Biomolecules, Irreversible thermodynamics. Energy dissipation. Living systems... 

The second law of thermodynamics means that the processes of energy transformation can occur spontaneously only provided that energy passes from its concentrated (ordered) form to a diffused (disordered) one. Such energy redistribution in the system is characterized by a quantity which has been named as entropy, which, as a function of state of the thermodynamic system (the more energy irreversible dissipates as heat, the higher entropy is. Whence it follows that any system whose properties change in time aspires to an equilibrium state at which the entropy of the system takes its maximum value. In this coimection, the second law of thermodynamics is often called the law of increasing entropy, and entropy (as a physical quantity or as a physical notion) is considered as a measure of disorder of a physicochemical system. 

The flow of matter and energy through an open system allows the system to self-organize, and to transfer entropy to the environment. This is the basis of the theory of dissipative structures, developed by Ilya Prigogine. He noted that self-organization can only occur far away from thermodynamic equilibrium [17]. 

Dissipative, open systems that allow for the flux of energy and matter may exhibit non-linear and complex behavior. Following the above argumentation, complex systems are usually far from thermodynamic equilibrium but, despite the flux, there may be a stable pattern, which may arise from small perturbations that cause a larger, non-proportional effect. These patterns can be stabilized by positive (amplifying)... 

The present analysis shows that when a thermodynamic gradient is first applied to a system, there is a transient regime in which dynamic order is induced and in which the dynamic order increases over time. The driving force for this is the dissipation of first entropy (i.e., reduction in the gradient), and what opposes it is the cost of the dynamic order. The second entropy provides a quantitative expression for these processes. In the nonlinear regime, the fluxes couple to the static structure, and structural order can be induced as well. The nature of this combined order is to dissipate first entropy, and in the transient regime the rate of dissipation increases with the evolution of the system over time. 

---