Improved Explicit Current–Voltage Model for Long-Channel Undoped Surrounding-Gate Metal Oxide Semiconductor Field Effect Transistor

Abstract

Using a Euclidean path integral representation for the canonical ensemble partition function we calculate the average value and fluctuations ofthe horizon area for thermal equilibrium black holes. The exciting prospect that black holes can have real thermodynamic properties was first seriously proposed by Bekenstein [l]. His proposals were later confirmed when Hawking 121 demonstrated that quantum effects lead to thermal radiation from black particular, Euclidean path integral representations for the partition functions have been developed. The pioneering contributions to these representations are those of Gibbons and Hawking [3] and York [4].The analysis by York [4] centres on the canonical ensemble. In the form appropriate for systems containing black holes, the canonical ensemble is defined by fixing the area A of some 2-sphere centred on the black hole and the inverse temperature p as measured on the same 2-sphere. From this definition a well defined canonical ensemble partition function Z(p, A) can be built. From Z ( p , A) can be extracted the canonical ensemble thermal equilibrium properties of black holes. The principal results of this paper are two formulae, one is for the average value of the area of the horizon (AH) and the other is for the fluctuations in (A,.,). The averaging is with respect to Z(p, A).Since Schwarzschild black holes have associated with them three types of horizons, me even1 nonzun, Lnc apparcnr nurrzun, an" LW LIIUC-IIXC-~iuiii suiia~ic {~C C L J J IUI

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