Thermodynamic fluctuation theory

According to the thermodynamic theory of fluctuations, the mean-square concentration fluctuation is given - by... 

Glansdorff, G., and I. Prigogine, Thermodynamic Theory of Structure, Stability and Fluctuations, Chapter 3, Wiley, London, 1971. 

P. Glansdorff and I. Progogine, Thermodynamic theory of Structure, Stability and Fluctuations, 1971, Wiley, New York. 

This principle is very general, relating neither to the linearity nor to the symmetry of the transport laws. On the other hand, it is difficult to attribute a physical meaning to dxP- The authors later attempted to derive a local potential from this property, and they applied this concept to the study of the chemical and hydrodynamical stability (e.g., the Benard convection). The results of this approach were published in Glansdorff and Prigogine s book Thermodynamic Theory of Structure, Stability and Fluctuations (LS.IO, 10a), published in 1971. 

In 1977. Professor Ilya Prigogine of the Free University of Brussels. Belgium, was awarded Ihe Nobel Prize in chemistry for his central role in the advances made in irreversible thermodynamics over the last ihrec decades. Prigogine and his associates investigated Ihe properties of systems far from equilibrium where a variety of phenomena exist that are not possible near or al equilibrium. These include chemical systems with multiple stationary states, chemical hysteresis, nucleation processes which give rise to transitions between multiple stationary states, oscillatory systems, the formation of stable and oscillatory macroscopic spatial structures, chemical waves, and Lhe critical behavior of fluctuations. As pointed out by I. Procaccia and J. Ross (Science. 198, 716—717, 1977). the central question concerns Ihe conditions of instability of the thermodynamic branch. The theory of stability of ordinary differential equations is well established. The problem that confronted Prigogine and his collaborators was to develop a thermodynamic theory of stability that spans the whole range of equilibrium and nonequilibrium phenomena. 

Glansdorff, P. Prigogine, I. "Thermodynamic Theory of Structure, Stability and Fluctuations" Interscience-Wiley, New York, 1971. 

Refs. [i] Prigogine I-Autobiography http //nobelprize.org/chemistry/ laureates/1977/prigogine [ii] Prigogine I (1967) Introduction to the thermodynamics of irreversible processes. Wiley Interscience, New York [iii] Prigogine I (1962) Non-equilibrium statistical mechanics. Wiley Interscience, New York [iv] Glansdorff P, Prigogine I (1971) Thermodynamic theory of structure stability and fluctuations. Wiley, London... 

From the perspective of the fluctuation-dissipation approach, Dewey (1996) proposed that the time evolution of a protein depends on the shared information entropy. S between sequence and structure, which can be described with a nonequilibrium thermodynamics theory of sequence-structure evolution. The sequence complexity follows the minimal entropy production resulting from a steady nonequilibrium state... 

Equation (12.24) does not describe the dynamics of thermodynamic fluctuations, although the nonequilibrium thermodynamics theory and the thermodynamic fluctuations are connected in deriving the Onsager rules. However, the introduction of the notion of internal degrees of freedom into nonequilibrium thermodynamics implicitly accounts for the fluctuations. 

Another approach is to employ rigorous statistical thermodynamic theories. In this paper, the Kirkwood-Buff (KB) theory of solutions (fluctuation theory of solutions) is employed to analyze the thermodynamics of multicomponent mixtures, with the emphasis on quaternary mixtures. This theory connects the macroscopic properties of re-component solutions, such as the isothermal compressibility, the concentration deriva-... 

One of the characteristic features of statistical mechanics is the treatment of fluctuations, whereas in thermodynamics we treat variables such as E, V, or N as having sharp values. Statistical mechanics acknowledge the fact that these quantities can fluctuate. The theory also prescribes a way of calculating the average fluctuation about the equilibrium values. 

Molecular fragments are the mutually open subsystems, which exhibit fluctuations in their electron densities and overall numbers of electrons. In chemistry one is interested in both the equilibrium distributions of electrons and non-equilibrium processes characterized by rates. Recently, it has been demonstrated [23] that the information theory provides all necessary tools for the local dynamical description of the density fluctuations and electron flows between molecular subsystems, which closely follows the thermodynamic theory of irreversible processes [146],... 

Glansdorff, P., I. Prigogine Thermodynamic Theory of Structure Stability and Fluctuations Wiley New York, 1971... 

GlansdorfF P, Prigogine I Thermodynamic theory of stmcture, stability and fluctuations, Wiley-Interscience, 1971. 

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