![]() ![]() Why q-expectation values must be used in nonextensive statistical mechanics. Mathematical Methods in Kinetic Theory (Plenum Press, New York, 1969).Ībe, S. Translation of Ludwig Boltzmann’s paper “On the relationship between the second fundamental theorem of the mechanical theory of heat and probability calculations regarding the conditions for thermal equilibrium” sitzungberichte der kaiserlichen akademie der wissenschaften. Superdiffusion and non-gaussian statistics in a driven-dissipative 2d dusty plasma. Tsallis non-extensive statistical mechanics of El Nino southern oscillation index. Experimental determination of the nonextensive entropic parameter q. Rotational dynamics of turbulence and tsallis statistics. Anomalous diffusion and tsallis statistics in an optical lattice. ![]() Option pricing formulas based on a non-gaussian stock price model. Border between regular and chaotic quantum dynamics. Anomalous diffusion and non-gaussian velocity distribution of hydra cells in cellular aggregates. Evidences for nonextensivity conjugation in hadronic scattering systems. Equilibrium distribution of heavy quarks in Fokker–Planck dynamics. Non-extensive statistical mechanics and particle spectra in elementary interactions. Is re-association in folded proteins a case of nonextensivity?. From gibbs microcanonical ensemble to tsallis generalized canonical distribution. A fresh take on disorder, or disorderly science?. Introduction to Nonextensive Statistical Mechanics: Approaching a Complex World (Springer, New York, 2009).Ĭho, A. Possible generalization of Boltzmann–Gibbs statistics. Quantification method of classification processes. The number N can be used for the physical measure of deviation from Boltzmann entropy. Here we show the entropy of the system composed of finite N molecules of ideal gas is Havrda–Charvát–Tsallis entropy or the q-entropy with the entropic index \(q=\frac\). Meanwhile, the derivation of the precise entropy formula for the Boltzmann’s system of N molecules seems unknown and hard to be accomplished by following his way because the infinity assumption is not allowed to use any more in this case. However, Boltzmann derived his entropy formula by considering a very fundamental physical system composed of infinite number of ideal gases where the infinity was an indispensable constraint for using Stirling’s approximation with respect to the factorial function that appeared in his procedure 21. The endeavors to discover additional factors that explain the roles of the entropic index q and to find empirical or approximated relations for the entropic index have been in various fields including physics, chemistry, and economics 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20. The generalisation is characterised by a single parameter known as the entropic index q and Boltzmann entropy is retrieved when q approaches one. The first appearance of the formula of the q-entropy is on the paper of Havrda and Charvát for the purpose of information entropy and Tsallis has rediscovered it for Boltzmann–Gibbs statistical mechanics. Moreover, if the reaction of the process is known then we can find by using a table of standard entropy values. If the happening process is at a constant temperature then entropy will be Derivation of Entropy Formula is the. R., 2010, Advanced Heat and Mass Transfer, Global Digital Press, Columbia, MO.Havrda–Charvát–Tsallis entropy or the q-entropy is a generalisation of Boltzmann entropy 1, 2, 3. Besides, there are many equations to calculate entropy: 1. The second law of thermodynamics requires that each of these entropy generations be greater than or equal to zero.įaghri, A., and Zhang, Y., 2006, Transport Phenomena in Multiphase Systems, Burlington, MA.įaghri, A., Zhang, Y., and Howell, J. The entropy generation for a control volume including Π phases consists of entropy generation in each phase, plus that in the interfaces. Thermodynamic definition of entropy Absorption of heat increases the entropy of the system while evaluation of heat decreases the value of S. If the control volume includes Π phases, the second law of thermodynamics must be obtained by integrating over the two phases separately (Faghri and Zhang, 2006), (3), one obtains the integral form of the second law of thermodynamics for single phase systems: The last term represents entropy generation, which should always be greater than or equal to zero, i.e.,Ĭombining eqs. (2), the first term represents the change of entropy due to heat transfer across the boundary of the control volume, and the second term represents the change of entropy due to internal heat generation in the control volume. The change of entropy in a closed system results from heat transfer and/or entropy generation: The entropy change for a system with fixed-mass and only one phase can be obtained by setting Φ = S,φ = s in eq. The second law of thermodynamics requires that the entropy generation in a closed system (fixed-mass) must be greater than or equal to zero. ![]()
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