Entropy transfer

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]. 

Distinguishing the created entropy deSrev from the transferred entropy dtSirT, we express the total change in entropy as the sum of the two parts shown in Fig. 3.2 and Eq. 3.12 ... 

This indicates that any irreversible process, if occurring at constant entropy S and pressure p, is accompanied by a decrease in the enthalpy from the initial high level Hjnijal toward the final low level Hfiml of the system. From the foregoing we see that the internal energy and enthalpy may play the role of thermodynamic potentials for an irreversible process if occurring under the condition of constant entropy S. This condition of constant entropy, however, is unrealistic because entropy S contains both created entropy Sirr and transferred entropy Sm. 

Transfer functions can also be defined for the other thermodynamic state functions. Since enthalpy changes are often conveniently measurable, the transfer enthalpy, is perhaps the most widely used function. From the second law of thermodynamics, the transfer entropy function is given by Equation 6.9. 

The transfer entropy (TE) has been introduced by Schreiber [6] as a measure to quantify information transfer between systems evolving in time. Let X and Y be two random variables representing the state transition of two stochastic or deterministic systems. Let Xf and yt be the values respectively of X and Y at time t. Let also suppose that the systems are Markovian processes of order 1, i.e. 

In this section we illustrate the results concerning the robustness of the results returned by the DCI method with respect to the variance introduced by the homogeneous system generation. We assessed the ranking of the RSs and the transfer entropy values as a function of a sampled distribution of homogeneous system instances and we also compared different ways for generating it. We first describe the test cases used in the analysis subsequently, we discuss the results in terms of RSs ranking and transfer entropy. 

Table 7. Transfer entropy T between RSs in the five test cases. The values in the table represent Ty x, where Y is the element in the column and X in the row.

---