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Quantum and Relativistic Corrections to Maxwell–Boltzmann Ideal Gas Model from a Quantum Phase Space Approach

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Abstract

The quantum corrections related to the ideal gas model often considered are those associated to the bosonic or fermionic nature of particles. However, in this work, other kinds of corrections related to the quantum nature of phase space are highlighted. These corrections are introduced as improvements in the expression of the partition function of an ideal gas. Then corrected thermodynamics properties of the ideal gas are deduced. Both the non-relativistic quantum and relativistic quantum cases are considered. It is shown that the corrections in the non-relativistic quantum case may be particularly useful to describe the deviation from the Maxwell–Boltzmann model at low temperature and/or in confined space. These corrections can be considered as including the description of quantum size and shape effects. For the relativistic quantum case, the corrections could be relevant for confined space and when the thermal energy of each particle is comparable to their rest energy. The corrections appear mainly as modifications in the thermodynamic equation of state and in the expressions of the partition function and thermodynamic functions like entropy, internal energy and free energy. Expressions corresponding to the Maxwell–Boltzmann model are shown to be asymptotic limits of the corrected expressions.

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Authors and Affiliations

  1. Institut National des Sciences et Techniques Nucléaires (INSTN- Madagascar), BP 3907, 101, Antananarivo, Madagascar

    Rivo Herivola Manjakamanana Ravelonjato, Ravo Tokiniaina Ranaivoson, Raoelina Andriambololona, Hanitriarivo Rakotoson & Naivo Rabesiranana

  2. Department of Physics, Faculty of Sciences – University of Antananarivo, BP 566, 101, Antananarivo, Madagascar

    Roland Raboanary, Hanitriarivo Rakotoson & Naivo Rabesiranana

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  1. Rivo Herivola Manjakamanana Ravelonjato
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  2. Ravo Tokiniaina Ranaivoson
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  3. Raoelina Andriambololona
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  4. Roland Raboanary
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  5. Hanitriarivo Rakotoson
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  6. Naivo Rabesiranana
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Contributions

All authors contributed to the study conception and design. The main calculations were performed by RHMR and RTR. RHMR, RTR and RA write together the first draft of the manuscript. The other authors commented and made corrections on previous versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Rivo Herivola Manjakamanana Ravelonjato.

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Ravelonjato, R.H.M., Ranaivoson, R.T., Andriambololona, R. et al. Quantum and Relativistic Corrections to Maxwell–Boltzmann Ideal Gas Model from a Quantum Phase Space Approach. Found Phys 53, 88 (2023). https://doi.org/10.1007/s10701-023-00727-5

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