Unnormalized nonextensive expectation value and zeroth law of thermodynamics
نویسندگان
چکیده
منابع مشابه
Validity of the second law in nonextensive quantum thermodynamics.
The second law of thermodynamics in nonextensive statistical mechanics is discussed in the quantum regime. Making use of the convexity property of the generalized relative entropy associated with the Tsallis entropy indexed by q, Clausius' inequality is shown to hold in the range q in (0, 2]. This restriction on the range of the entropic index, q, is purely quantum mechanical and there exists n...
متن کاملNecessity of q-expectation value in nonextensive statistical mechanics.
In nonextensive statistical mechanics, two kinds of definitions have been considered for expectation value of a physical quantity: one is the ordinary definition and the other is the normalized q-expectation value employing the escort distribution. Since both of them lead to the maximum-Tsallis-entropy distributions of a similar type, it is of crucial importance to determine which the correct p...
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Tsallis' thermostatistics [1–14] is by now recognized as a new paradigm for statistical mechanical considerations. However, the generalization of thermo-dynamics' zero-th law to a nonextensive scenario is plagued by difficulties [2]. In this work we suggest a way to overcome this problem.
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Within the Tsallis thermodynamics framework, and using scaling properties of the entropy, we derive a generalization of the Gibbs-Duhem equation. The analysis suggests a transformation of variables that allows standard thermodynamics to be recovered. Moreover, we also generalize Einstein's formula for the probability of a fluctuation to occur by means of the maximum statistical entropy method. ...
متن کاملA mathematical proof of the zeroth "law" of thermodynamics and the nonlinear Fourier "law" for heat flow.
What is now known as the zeroth "law" of thermodynamics was first stated by Maxwell in 1872: at equilibrium, "Bodies whose temperatures are equal to that of the same body have themselves equal temperatures." In the present paper, we give an explicit mathematical proof of the zeroth "law" for classical, deterministic, T-mixing systems. We show that if a body is initially not isothermal it will i...
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ژورنال
عنوان ژورنال: Chaos, Solitons & Fractals
سال: 2003
ISSN: 0960-0779
DOI: 10.1016/s0960-0779(02)00137-6