Time-fractional heat equations and negative absolute temperatures
نویسندگان
چکیده
منابع مشابه
Inconsistent thermostatistics and negative absolute temperatures
A considerable body of experimental and theoretical work claims the existence of negative absolute temperatures in spin systems and ultra-cold quantum gases. Here, we clarify that such findings can be attributed to the use of a popular yet inconsistent entropy definition, which violates fundamental thermodynamic relations and fails to produce sensible results for simple analytically tractable c...
متن کاملThe Physics of Negative Absolute Temperatures
Negative absolute temperatures were introduced into experimental physics by Purcell and Pound, who successfully applied this concept to nuclear spins; nevertheless the concept has proved controversial : a recent article aroused considerable interest by its claim, based on a classical entropy formula (the ‘volume entropy’) due to Gibbs, that negative temperatures violated basic principles of sta...
متن کاملComment on “ Consistent thermostatistics forbids negative absolute temperatures ”
In their paper [1], Dunkel and Hilbert argue that negative absolute temperatures, a wellestablished thermodynamic concept, are inconsistent with thermodynamics. They claim to “prove that all previous negative temperature claims and their implications are invalid as they arise from the use of an entropy definition that is inconsistent both mathematically and thermodynamically”. Here we point out...
متن کاملStrichartz Type Estimates for Fractional Heat Equations
We obtain Strichartz estimates for the fractional heat equations by using both the abstract Strichartz estimates of Keel-Tao and the HardyLittlewood-Sobolev inequality. We also prove an endpoint homogeneous Strichartz estimate via replacing L∞x (R ) by BMOx(R) and a parabolic homogeneous Strichartz estimate. Meanwhile, we generalize the Strichartz estimates by replacing the Lebesgue spaces with...
متن کاملDIFFERENTIAL TRANSFORMATION METHOD FOR SOLVING FUZZY FRACTIONAL HEAT EQUATIONS
In this paper, the differential transformation method (DTM) was applied to solve fuzzy fractional heat equations. The elementary properties of this method were given. The approximate and exact solutions of these equations were calculated in the form of series with easily computable terms. The proposed method was also illustrated by some examples. The results revealed that DTM is a highly effect...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Computers & Mathematics with Applications
سال: 2014
ISSN: 0898-1221
DOI: 10.1016/j.camwa.2013.11.007