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## Entropy Meters and the Entropy of Non-extensive Systems (2014)

### Citations

561 |
Possible generalization of Boltzmann-Gibbs statistics
- Tsallis
- 1988
(Show Context)
Citation Context ...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 ... |

49 | The physics and mathematics of the second law of thermodynamics,
- Lieb, Yngvason
- 1999
(Show Context)
Citation Context ...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... |

23 | The second law, - Atkins - 1994 |

21 | A Guide to Entropy and the Second Law of Thermodynamics
- Lieb, Yngvason
- 1998
(Show Context)
Citation Context ... 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... |

18 |
Mathematical Foundations of Thermodynamics
- Giles
- 1964
(Show Context)
Citation Context ...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... |

16 | A Fresh Look at Entropy and the Second Law of Thermodynamics’, Physics Today (April issue); math-ph/0003028 - Lieb, Yngvason - 2000 |

11 | The entropy of classical thermodynamics - Lieb, Yngvason - 2003 |

7 |
The second laws of quantum thermodynamics.
- Brandao, Horodecki, et al.
- 2015
(Show Context)
Citation Context ...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... |

5 |
Rigorous and general definition of thermodynamic entropy
- Beretta, Zanchini
- 2011
(Show Context)
Citation Context ...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... |

5 |
Laws of thermodynamics beyond the von Neumann regime”, arXiv:1207.0434 [quant-ph
- Egloff, Dahlsten, et al.
- 2012
(Show Context)
Citation Context ...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... |

4 |
Fundamental limitations for quantum and nano thermodynamics
- Horodecki, Oppenheim
- 2011
(Show Context)
Citation Context ...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... |

4 | The entropy concept for nonequilibrium states
- Lieb, Yngvason
(Show Context)
Citation Context ...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... |

3 | The Entropy Principle: Thermodynamics for the Unsatisfied - Thess - 2011 |

2 |
2011 Superstatistics in nanoscale electrochemical systems
- Garćıa-Morales, Krischer
- 1953
(Show Context)
Citation Context ...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... |

1 |
Entropy in Non Traditional Systems, private communication
- Badiali, Kaabouchi
- 2013
(Show Context)
Citation Context ...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... |

1 |
2nd ed. 2005 Thermodynamics: foundations and applications
- Gyftopoulos, Beretta
- 1991
(Show Context)
Citation Context ...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... |