Both Boltzmann's and Gibbs's definitions of entropy are used. The properties of the studied systems are evaluated numerically but exactly; this means that Stirling's approximation was not used in the calculation and that the discrete nature of energy was taken into account. Results show that, ...
In this work, we demonstrate the inappropriateness of the Boltzmann-Gibbslog-formulation of the physical Clausius entropy $S$ in connectingthermodynamics and phase space statistics. To achieve our goal, we studythermodynamically the simple case of ideal gases embedded in a finite heat bathand compare...
E.g., see the remarks in ([1], p. 76 n. 5 who emphatically references Gibbs), ([113], pp. 39–40) as well as those in [115], Sect.2where the authors attempt to connect what is sometimes called Boltzmann’s combinatorial entropy formula (i.e.,\({S}_{B}(X)=k\, \mathrm{...
Gibbs 3 also arrived, by considering purely empirical facts, at the following conclusion: "The impossibility of an incompensated decrease of entropy seems to be reduced to an improbability". 1. Helmholtz, Berlin Ber. 17, 172 (1884). 2. Boltzmann, Vorlesungen fiber Gastheorie 1, p. 61 [...
{i}\rangle). To obtain an estimate of the same quality via Gibbs sampling according to (5), we would then need on the order ofτθRcorrelated Markov-chain samples (see, for example, Sec. 2 of ref.34and also Methods). Hence the (minimal) value ofτθ = 1 hints at independent...
Arrhenius方程:k=k?exp(Ea/RT)Boltzmann方程:S=klnΩGibbs方程:ΔG=ΔH-TΔS平衡常数和Gibbs自由能转换:ΔG=-RTlnK电化学方程:ΔG=-zFE晶体密度计算公式:D=ZM/abcsinANA quantum 分享4赞 低调奋进吧 kaifang1987 湖北省2011年优秀博士学位论文获奖名单工艺规划与车间调度集成问题的求解方法研究 李新宇 邵...
Boltzmann Entropy: S = k log W Gibbs entropy information theory Shannon’s entropy Shannon’s entropy Shannon: “I thought of calling it “information”. But the word was overly used, so I decided to call it “uncertainty”. When I discussed it with John von Neumann, he had a better id...
The Gibbs entropy of a macroscopic classical system is a function of a probability distribution over phase space, i.e., of an ensemble. In contrast, the Boltzmann entropy is a function on phase space, and is thus defined for an individual system. Our aim is to discuss and compare these ...
In the 1950's and early 1960's there was a great deal of activity trying to develop a theory of irreversible processes in terms of the notion of local entropy production. For a time it appeared that this conception might be justified in statistical theory. However, these arguments (de ...
The long-standing contrast between Boltzmann's and Gibbs' approach to statistical thermodynamics has been recently rekindled by Dunkel and Hilbert, who criticize the notion of negative absolute temperature (NAT) as a misleading consequence of Boltzmann's definition of entropy. A different definition, ...