Entropy due to irreversible processes

Nonequilibrium thermodynamics estimates the rate of entropy production for a process. This estimation is based on the positive and definite entropy due to irreversible processes and of Gibbs relation... 

Fig. 8.2 A self-organising system needs a flow of energy. To continuously overcome the loss of entropy due to irreversible processes, it must be coupled to a flow delivering energy in a low entropy form and dissipate it under the form of heat or inactivated chranical derivatives...

In an advancing irreversible process such as a mechanical movement of a body, dissipation of energy for instance from a mechanical form to a thermal form (frictional heat) takes place. The second law of thermodynamics defines the energy dissipation due to irreversible processes in terms of the creation of entropy Slrr or the creation of uncompensated heat Qirr. 

Therefore, the total entropy produced within the system must be discharged across the boundary at stationary state. For a system at stationary state, boundary conditions do not change with time. Consequently, a nonequilibrium stationary state is not possible for an isolated system for which deS/dt = 0. Also, a steady state cannot be maintained in an adiabatic system in which irreversible processes are occurring, since the entropy produced cannot be discharged, as an adiabatic system cannot exchange heat with its surroundings. In equilibrium, all the terms in Eq. (3.48) vanish because of the absence of both entropy flow across the system boundaries and entropy production due to irreversible processes, and we have dJS/dt = d dt = dS/dt = 0. 

Second-law analysis can determine the level of energy dissipation from the rate of entropy production in the system. The entropy production approach is especially important in terms of process optimality since it allows the entropy production of each process to be determined separately. The map of the volumetric entropy production rate identifies the regions within the system where excessive entropy production occurs due to irreversible processes. Minimizing of excessive irreversibilities allows a thermodynamic optimum to be achieved for a required task. Estimation of the trade-offs between the various contributions to the rate of entropy production may be helpful for attaining thermodynamically optimum design and operation. 

The form of (6.2.15) and (6.2.18) is highly significant. In each case the rate of local entropy density generation, due to irreversible processes occurring totally within a local volume element, may be written as a sum of terms of the general form i wherein the Ji represent either general... 

Our object now is to evaluate the entropy production d S due to irreversible processes inside the system. This is achieved by applying Gibbs equation to each chamber. Thus, for chamber I, we have... 

Now our object would be to evaluate entropy production dj due to irreversible processes inside the system, which are simply the transport of matter and electricity. The total entropy production d6 due to internal as well as external factors would be given by... 

Photosynthetic processes have the main responsibility of energy transfer in biological systems. This is possible because living systems are open systems, otherwise, the free energy F would not be available. In open systems, variations of entropy can be the consequence of different processes dgS, is the entropy exchanged with the environment, and dtS, is the entropy variation due to irreversible processes within the system. The second term is clearly positive, but the first term does not have a definite sign. So the inequality of Clausius-Carnot becomes ... 

Figure 3.7 Entropy changes in a system consist of two parts d S due to irreversible processes, and dgS, due to exchange of energy and matter. According to the second law, the change diS is always positive. The entropy change d S can be positive or negative...

We have already seen that all isolated systems evolve to the state of equilibrium in which the entropy reaches its maximum value. This is the basic extremum principle of thermodynamics. But we don t always deal with isolated systems. In many practical situations, the physical or chemical system under consideration is subject to constant pressure or temperature or both. In these situations the positivity of entropy change due to irreversible processes, diS > 0, can also be expressed as the evolution of certain thermodynamic functions to their... 

As we have seen in the previous chapter, due to irreversible processes, the entropy of an isolated system continues to increase (diS > 0) until it reaches the maximum possible value. The state thus reached is the state of equilibrium. Therefore, when U and V are constant, every system evolves to a state of maximum entropy. 

Through these relations, the change of the thermodynamic potentials AF, AG or AH due to a fluctuation can be related to the entropy production Aj S. The system is stable to all fluctuations that result in Aj 5 < 0, because they do not correspond to the spont eous evolution of a system due to irreversible processes. From the above relations it is clear how one could also characterize stability of the equilibrium state by stating that the system is stable to fluctuations for which AF > 0, AG > 0 or AH > 0. For fluctuations in the equilibrium state, these conditions can be written more explicitly in terms of the second-order variations 6 V > 0,5 G > 0 and d H > 0, which in turn can be expressed using the. second-order derivatives of these potentials. The conditions for stability obtained in this way are identical to those obtained in Chapter 12. 

In our more general approach, the main task is to obtain an expression for the entropy production Ai5 associated with a fluctuation. A system is stable to fluctuations if the associated Ai < 0. In Chapter 3 we have seen that the general form of entropy production due to irreversible processes takes the quadratic form... 

Also, the entropy production due to chemical reactions in each phase should be separately positive.) Thus, the symmetry principle provides constraints for the coupling of, and the entropy production due to, irreversible processes. 

In the above, PP(t) = diS(t)/dt is the entropy production due to irreversible processes inside the system and P (/) = dsS(t)/dt is the entropy production due to entropy flow across the boundary between the system and its surroundings. 

Natural phenomena are striking us every day by the time asymmetry of their evolution. Various examples of this time asymmetry exist in physics, chemistry, biology, and the other natural sciences. This asymmetry manifests itself in the dissipation of energy due to friction, viscosity, heat conductivity, or electric resistivity, as well as in diffusion and chemical reactions. The second law of thermodynamics has provided a formulation of their time asymmetry in terms of the increase of the entropy. The aforementioned irreversible processes are fundamental for biological systems which are maintained out of equilibrium by their metabolic activity. 

THOMSON PRINCIPLE. The hypothesis that, if thermodynamically reversible and irreversible processes take place simultaneously in a system, the laws of thermodynamics may be applied to the reversible process while ignoring for this purpose the creation of entropy due to die irreversible process. Applied originally by Thomson to the case of... 

First of all, we will touch a widely believed misunderstanding about impossibility of using the second law of thermodynamics in the analysis of open systems. Surely, the conclusion on inevitable degradation of isolated systems that follows from the second law of thermodynamics cannot be applied to open systems. And particularly unreasonable is the supposition about thermal death of the Universe that is based on the opinion of its isolation. The entropy production caused by irreversible energy dissipation is, however, positive in any system. Here we have a complete analogy with the first law of thermodynamics. Energy is fully conserved only in the isolated systems. For the open systems the balance equalities include exchange components which can lead to the entropy reduction of these systems at its increase due to internal processes as well. 

In a general case of an open system, at a given point with space coordi nate r a set of different irreversible processes can occur simultaneously with a total of entropy increment density dis(r, t) > 0. In this situation, the overall entropy increment due to internal processes in the entire system is expressed by integral... 

Equation (1.17) is valid for the case of an open system, too—that is, when its Gibbs potential can be additionally varied throughout the flow or during the inflow of matter. Therefore, the rate of entropy production due to irreversible internal processes is... 

---