GLOBAL CHANGES IN ENTROPY

The conformational entropy of compound 7 was calculated by converting their respective energy profiles into probability functions. First the global change in dAG° (difference in affinity) for tetralin 7 relative to 4 is significant 15.5kJ/mol. From the calculations with the Shannon... 

Some of the previous articles have inspired several investigations on the relation between entropy and chemical change. In work by Bernstein and Levine (1972) optimal means of characterizing the distribution of product energies were discussed in terms of an information measure / (see e.g. Jaynes, 1963, Katz. 1967 for uses of 1 in thermodynamical problems). Global, detailed experiments provide average transition probabilities ru(A, B), from which the surprisal A, B) is defined to be... 

The change of total entropy is dS = dgS + diS. The term deS is the entropy exchange through the boundary, which can be positive, zero, or negative, while the term diS is the rate of entropy production, which is always positive for irreversible processes and zero for reversible ones. The rate of entropy production is diS/dt = JkXk. A near-equilibrium system is stable to fluctuations if the change of entropy production is negative, i.e. Ai5 < 0. For isolated systems, dS/dt > 0 shows the tendency toward disorder as d S/dt = 0 and dS = diS > 0. For nonisolated systems, diS/dt > 0 shows irreversible processes, such as chemical reactions, heat conduction, diffusion, or viscous dissipation. For states near global equilibrium, d S is a bilinear form of flows and forces that are related in linear form. 

Classical thermodynamics deals with equilibrium states. Entropy changes are then calculated via reversible processes. By contrast, non-equilibrium thermodynamics deals with systems that are not in global equilibrium. The entropy production can then be calculated from actual fluxes and forces. Real systems, for instance in biology or in industry, are not in equilibrium and are of course more interesting. Transport phenomena are always irreversible, and we shall see how they are contained in non-equilibrium thermodynamics. The list a to e below gives the main reasons for why non-equilibrium thermodynamics is important. 

To account for the effect of n chiral centers, a global symmetry number, gi ext int is defined, so that the change in standard entropy due to symmetry changes associated with the transformation of the reactant into the activated complex is written ... 

Entropy in an isolated system increases dS/dt> 0 until it reaches equilibrium dS/dt = 0, and displays a direction of change leading to the thermodynamic arrow of time. The phenomenological approach favoring the retarded potential over the solution to the Maxwell field equation is called the time arrow of radiation. These two arrows of time lead to the Einstein-Ritz controversy Einstein believed that irreversibility is based on probability considerations, while Ritz believed that an initial condition and thus causality is the basis of irreversibility. Causality and probability may be two aspects of the same principle since the arrow of time has a global nature. 

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