Equilibrium states and thermodynamic potentials

When the system is out of full thermodynamic equilibrium, its non-equilibrium state may be characteristic of it with gradients of some parameters and, therefore, with matter and/or energy flows. The description of the spontaneous evolution of the system via non equilibrium states and prediction of the properties of the system at, e.g., dynamic equilibrium is the subject of thermodynamics of irreversible (non-equilibrium) processes. The typical purposes here are to predict the presence of solitary or multiple local stationary states of the system, to analyze their properties and, in particular, stability. It is important that the potential instability of the open system far from thermodynamic equilibrium, in its dynamic equilibrium may result sometimes in the formation of specific rather organized dissipative structures as the final point of the evolution, while traditional classical thermodynamics does not describe such structures at all. The highly organized entities of this type are living organisms. 

In the equilibrium state, the anodic and cathodic partial reactions of an electrochemical reaction have equal rates. The system is in a dynamic equilibrium state, and no net reaction occurs. For example, when a copper sheet is immersed in copper sulfate solution, in the equilibrium state the anodic dissolution rate of copper from sheet to solution equals the cathodic deposition rate from the solution to the surface of the sheet. Theoretically, one can calculate the equilibrium state of an electrochemical reaction from thermodynamic values. This is the standard electrode potential, E°, or equilibrium potential of the electrochemical reaction. The standard electrode potential corresponds to a determined standard state of 0.1 MPa, 25 °C, activity of reactive species of 1 or ideal solution of 1.0 mol L-1, and equilibrium potential of any other state. 

In thermodynamics, a metastable equilibrium state has at least three constraints. Two of these constraints apply to a stable equilibrium state, and the third prevents the system from achieving that state. On releasing the third constraint the system experiences a spontaneous process and achieves the stable equilibrium state. We have seen two examples so far, in Figures 4.1 and 4.6. These examples were chosen to follow from our definition of entropy, and show spontaneous processes having no overall energy change in the system. They show entropy acting as a thermodynamic potential. 

It is important that with first-order phase transitions the thermodynamic potentials of both the phases are defined on both the sides of transition (see h igure l.lfiad), with the potential of one phase having a lower value (the equilibrium state) and that of the other pha.se having a higher value (the inetjistable state). 

Note that the two-directional arrows in these reaction expressions indicate that aU these reactions are chemically or electrochemically reversible, although they are not thermodynamically reversible due to their limited reaction rate in both reaction directions. Assuming that these reactions are in equilibrium states, the thermodynamic electrode potentials for the half-electrochemical Reactions (1.1) and (l.II) and the overall Reaction (1. III) can be expressed using the following Nemst equations ... 

The general theoretical treatment of ion-selective membranes assumes a homogeneous membrane phase and thermodynamic equilibrium at the phase boundaries. Obvious deviations from a Nemstian behavior are explained by an additional diffusion potential inside the membrane. However, allowing stationary state conditions in which the thermodynamic equilibrium is not established some hitherto difficult to explain facts (e.g., super-Nemstian slope, dependence of the selectivity of ion-transport upon the availability of co-ions, etc.) can be understood more easily. 

Redox potential (thermodynamic derivation). Suppose we take an electrochemical cell represented by Fig. 2.7. We shall now address the question of both the potential values and the equilibrium state that can be finally attained... 

For obvious reasons, we need to introduce surface contributions in the thermodynamic framework. Typically, in interface thermodynamics, the area in the system, e.g. the area of an air-water interface, is a state variable that can be adjusted by the observer while keeping the intensive variables (such as the temperature, pressure and chemical potentials) fixed. The unique feature in selfassembling systems is that the observer cannot adjust the area of a membrane in the same way, unless the membrane is put in a frame. Systems that have self-assembly characteristics are conveniently handled in a setting of thermodynamics of small systems, developed by Hill [12], and applied to surfactant self-assembly by Hall and Pethica [13]. In this approach, it is not necessary to make assumptions about the structure of the aggregates in order to define exactly the equilibrium conditions. However, for the present purpose, it is convenient to take the bilayer as an example. 

Here, we want to emphasize that The correct way to find the ground state of the homogeneous neutral u, d quark matter is to minimize the thermodynamical potential along the neutrality line Q nQ=o = Qu,d,e nQ=o> not like in the flavor asymmetric quark system, where (3-equilibrium is required but pe is a free parameter, and the ground state is determined by minimizing the thermodynamical potential klu,d,e-... 

In [25, 26] it is shown that at given pq the diquark gap is independent of the isospin chemical potential for Pi ) < Pic(Pq), otherwise vanishes. Increase of isospin asymmetry forces the system to pass a first order phase transition by tunneling through a barrier in the thermodynamic potential (2). Using this property we choose the absolute minimum of the thermodynamic potential (2) between two /3-equilibrium states, one with and one without condensate for the given baryochemical potential Pb = Pu + 2pd-... 

The first chair of theoretical physics in France was the professorship established for Pierre Duhem in 1894 at the Bordeaux Faculty of Sciences. 1 Duhem was well known in French scientific circles not only as a physicist but as a physicist of exceptional mathematical skills who addressed himself early in his scientific studies to chemical problems. He wrote a controversial doctoral thesis (1886) in which he developed the concept of thermodynamic potential for chemistry and physics, and he later developed a treatment of equilibrium processes formally analogous to the mechanics of Lagrange. The goal was to make mechanics a branch of the more general science of thermodynamics, a science that embraces "every change of qualities, properties, physical state, chemical constitution. "2... 

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