CAVINA, Vasco ; University of Luxembourg > Faculty of Science, Technology and Medicine > Department of Physics and Materials Science > Team Massimiliano ESPOSITO
SORET, Ariane ; University of Luxembourg > Faculty of Science, Technology and Medicine > Department of Physics and Materials Science > Team Massimiliano ESPOSITO
ASLYAMOV, Timur ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Physics and Materials Science (DPHYMS)
Ptaszynski, Krzysztof
ESPOSITO, Massimiliano ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Physics and Materials Science (DPHYMS)
External co-authors :
yes
Language :
English
Title :
Symmetry Shapes Thermodynamics of Macroscopic Quantum Systems
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Formally, when we say that a group (Equation presented) acts on the Hilbert space of the system (Equation presented), we mean that there is a group homomorphism between (Equation presented) and (Equation presented), the group of linear invertible operators acting on (Equation presented). To simplify the notation, we will never explicitly write this homomorphism and just treat (Equation presented) as a subgroup of (Equation presented). With this in mind, the elements of (Equation presented) will be accompanied by a hat to remark that they are operators acting on (Equation presented).
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The domain of (Equation presented) depends on the group of interest. In the case of the group (Equation presented) it takes the form of a vector, as we will see later.
See Ref. [35].
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We note that in the literature one often considers systems with collective dissipation processes (due to their computational simplicity), whose evolution preserves the probabilities (Equation presented) [19,25]. In such systems all entropy changes in time are subextensive with the system size.
The number of distinct irreducible representations of a group corresponds to the number of conjugacy classes of that group [36]. For (Equation presented) and for abelian groups in general this corresponds to the number of elements of the group.
This is motivated by the empirical observation that many physical systems display a well-defined macroscopic thermodynamics. If the ground state energy is subextensive, our approach still applies, with (Equation presented) going to zero. Situations where the ground-state energy is superextensive have no well-defined macroscopic thermodynamics, as commonly observed in systems with long-range interactions.
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