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...s, according to Theorem 1 below. Additivity is not always fulfilled for entropy functions that have been proposed as generalization of the Boltzmann-Gibbs entropy in statistical physics, as, e.g., in =-=[16]-=- and [6]. A relation between states in thermodynamics characterized by such an entropy can therefore not be the same as the one considered in the present paper. 2 Basic Definition of Entropy We start ...

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...em. The definition of temperature in a non-normal system is not at all obvious. Our entropy meter assumes none of these things and is based, instead, on the relation of adiabatic accessibility, as in =-=[11]-=-. R. Giles’s work [7] is a precursor of ours, as we stated in [11], but his definition of entropy for general systems, while similar in spirit, is not the same as the one described here or in [14]. An...

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... principle, with the aid of an ‘entropy meter’. An entropy meter can also be used to determine entropy functions for non-equilibrium states and mesoscopic systems. 1 Introduction In our previous work =-=[10]-=-–[14] (see also [15]) we showed how to define the entropy of ‘normal systems’ in equilibrium that are scalable, and showed that this entropy is essentially unique. It was derived without introducing t...

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...temperature in a non-normal system is not at all obvious. Our entropy meter assumes none of these things and is based, instead, on the relation of adiabatic accessibility, as in [11]. R. Giles’s work =-=[7]-=- is a precursor of ours, as we stated in [11], but his definition of entropy for general systems, while similar in spirit, is not the same as the one described here or in [14]. Another step in the dir...

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...creasingly “fuzzy” when the size of the system approaches atomic dimensions and the possibility of quantum entanglement between a system and its surroundings has to be taken into account. (See, e.g., =-=[3, 5, 9]-=-.) In such extreme situations our framework will eventually cease to apply, but there is still a wide intermediate range of 3 sizes above atomic scales where a non-extensive entropy in the sense of th...

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...to identify entropy as a quantity that allows us to decide which states can be transformed, adiabatically, into which other states. Here we recall that an adiabatic process for us is a ‘work process’ =-=[8, 4]-=- and does not require adiabatic enclosures 2 or slow motion or any such constraints. We do not want to introduce heat or temperature ab initio, and thus require only that changes in an adiabatic proce...

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...creasingly “fuzzy” when the size of the system approaches atomic dimensions and the possibility of quantum entanglement between a system and its surroundings has to be taken into account. (See, e.g., =-=[3, 5, 9]-=-.) In such extreme situations our framework will eventually cease to apply, but there is still a wide intermediate range of 3 sizes above atomic scales where a non-extensive entropy in the sense of th...

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...creasingly “fuzzy” when the size of the system approaches atomic dimensions and the possibility of quantum entanglement between a system and its surroundings has to be taken into account. (See, e.g., =-=[3, 5, 9]-=-.) In such extreme situations our framework will eventually cease to apply, but there is still a wide intermediate range of 3 sizes above atomic scales where a non-extensive entropy in the sense of th...

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...ciple, with the aid of an ‘entropy meter’. An entropy meter can also be used to determine entropy functions for non-equilibrium states and mesoscopic systems. 1 Introduction In our previous work [10]–=-=[14]-=- (see also [15]) we showed how to define the entropy of ‘normal systems’ in equilibrium that are scalable, and showed that this entropy is essentially unique. It was derived without introducing the co...

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...ing to Theorem 1 below. Additivity is not always fulfilled for entropy functions that have been proposed as generalization of the Boltzmann-Gibbs entropy in statistical physics, as, e.g., in [16] and =-=[6]-=-. A relation between states in thermodynamics characterized by such an entropy can therefore not be the same as the one considered in the present paper. 2 Basic Definition of Entropy We start with a v...

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...imilar in spirit, is not the same as the one described here or in [14]. Another step in the direction of a definition of entropy for general systems has been taken by J.P. Badiali and A. El Kaabouchi =-=[2]-=- who consider systems having scaling properties with fractional exponents and satisfying modifications of the axioms of [11]. Comment: The word ‘meter’ as used in our paper is a bit unusual in the sen...

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...to identify entropy as a quantity that allows us to decide which states can be transformed, adiabatically, into which other states. Here we recall that an adiabatic process for us is a ‘work process’ =-=[8, 4]-=- and does not require adiabatic enclosures 2 or slow motion or any such constraints. We do not want to introduce heat or temperature ab initio, and thus require only that changes in an adiabatic proce...