The thermodynamic properties of hydrophobic hydration processes have been analyzed and assessed. The thermodynamic binding functions result to be related to each other by the mathematical relationships of an ergodic algorithmic model (EAM). The active dilution dA of species A in solution is expressed as dA = 1/(Φ·xA) with thermal factor Φ = T–(Cp,A/R) and (1/xA) = did(A), where did(A) = ideal dilution. Entropy function is set as S = f(did(A),T). Thermal change of entropy (i.e., entropy intensity change) is represented by the equation (dS)d = Cp dln T. Configuration change of entropy (i.e., entropy density change) is represented by the equation (dS)T = (−R dln xA)T = (R dln did(A))T. Because every logarithmic function in thermodynamic space corresponds to an exponential function in probability space, the sum functions ΔHdual = (ΔHmot + ΔHth) and ΔSdual = (ΔSmot + ΔSth) of the thermodynamic space give birth, in exponential probability space, to a dual-structure partition function {>DS-PF}: exp(−ΔGdual/RT) = Kdual = (Kmot·ζth) = {(exp(−ΔHmot/RT))(exp(ΔSmot/R))}·{exp(−ΔHth/RT) exp(ΔSth/R)}. Every hydrophobic hydration process can be represented by {>DS-PF} = {>M-PF}·{>T-PF}, indicating biphasic systems. {>M-PF} = f(T,did(A)), concerning the solute, is monocentric and produces changes of entropy density, contributing to free energy −ΔGmot, whereas {>T-PF} = g(T), concerning the solvent, produces changes of entropy intensity, not contributing to free energy.Entropy density and entropy intensity are equivalent and summed witheach other (i.e., they are ergodic). From the dual-structure partitionfunction {>DS-PF}, the ergodic algorithmicmodel (EAM) can be developed. The model EAM consists of a set of mathematicalrelationships, generating parabolic convoluted binding functions R ln Kdual = −ΔGdual/T = {f(1/T)*g(T)} and RT ln Kdual =−ΔGdual = {f(T)*g(ln T)}. The first function in each convoluted couple f(1/T) or f(T)is generated by {>M-PF}, whereas thesecond function, g(T) or g(ln T), respectively, is generatedby {>T-PF}. The mathematical propertiesof the thermodynamic functions of hydrophobic hydration processes,experimentally determined, correspond to the geometrical propertiesof parabolas, with constant curvature amplitude Campl = 0.7071/ΔCp,hydr. The dual structure of the partition function conformsto the biphasic composition of every hydrophobic hydration solution,consisting of a diluted solution, with solvent in excess at constantpotential.
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机译：疏水水合过程的热力学性质已得到分析和评估。热力学结合函数的结果是通过遍历算法模型（EAM）的数学关系相互关联。物种A在溶液中的有效稀释度dA表示为dA = 1 /（Φ·xA），热因子Φ= T –（Cp，A / R），而（1 / xA）= do （A），其中did（A）=理想稀释度。熵函数设置为S = f（did（A），T）。熵的热变化（即，熵强度变化）由等式（dS）d = C p dln T 表示。熵的构型变化（即熵密度变化）由等式（d S ）T =（- R dln x A）表示T =（ R dln d id（A）） T 。因为热力学空间中的每个对数函数都对应于概率空间中的指数函数，所以和函数Δ H dual =（Δ H mot +Δ H th ）和Δ S dual =（Δ S mot热力学空间的 +Δ S th ）在指数概率空间中产生对偶结构分配函数{ > DS -PF }：exp（-Δ G dual / RT ）= K dual =（ K mot ·ζ th ）= {（exp（-Δ H < / em> mot / RT ））（exp（Δ S mot / R ））}·{exp（-Δ H th / RT ）exp（Δ S th / R ）}。每个疏水水合过程都可以用{ > DS-PF } = { > M-PF }·{< em> > T-PF }，表示双相系统。 { > M-PF } = f （ T ， d id （A））关于溶质，是单中心的，会产生熵密度的变化，从而导致自由能-Δ G mot ，而{ > T-PF } = g （ T ），与溶剂有关，会产生熵强度的变化，而无助于自由能。熵密度和熵强度相等并相加彼此（即它们是遍历的）。从双重结构分区函数{ > DS-PF }，遍历算法可以开发模型（EAM）。 EAM模型由一组数学模型组成关系，生成抛物线卷积绑定函数 R ln K dual =-Δ G dual / T = { f （1 / T ）* g （ T ）}和 RT ln K dual =−Δ G dual = { f （ T ）* g （ln < em> T ）}。每个卷积对 f （1 / T ）或 f （ T ）中的第一个函数由{ > M-PF }生成，而第二个函数分别生成 g （ T ）或 g （ln T ）由{ > T-PF }。数学性质疏水水化过程的热力学功能实验确定，对应于几何特性常数曲率振幅 C ampl = 0.7071 /Δ C p ，水合物的抛物线子>。分区函数的双重结构符合每种疏水水合溶液的两相组成由稀释溶液组成，不断有过量溶剂潜在。
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