Ensemble fluctuations related to generalized (probability-dependent) entropies and their work fluctuation theorem

• Published in: European physical journal plus 2022-03, Vol.137 (3), p.342, Article 342
• Main Authors: López-Picón, J. L., Obregón, O., Ríos-Padilla, J.
• Format: Article
• Language: English
• Subjects: Applied and Technical Physics; Atomic; Complex Systems; Condensed Matter Physics; Energy; Entropy; Equilibrium; Fluctuations; Mathematical and Computational Physics; Molecular; Optical and Plasma Physics; Physics; Physics and Astronomy; Probability; Regular Article; Statistical mechanics; Temperature; Theorems; Theoretical; Thermodynamics
• ISSN: 2190-5444; 2190-5444
• DOI: 10.1140/epjp/s13360-022-02527-8

The generalized theory of fluctuations corresponding to probability-dependent generalized entropies in the canonical and grand canonical ensembles is formulated. The entropies considered here depend on no other parameter than probability and were derived within the superstatistics approach. Since fluctuations can be expressed in terms of the thermodynamic heat capacity, these thermodynamic functions are sensitive to the non-extensive effects conferred by the new entropies. The differences in standard and generalized fluctuations are computed from the thermodynamics of Mie fluids from which the range dependence of generalized fluctuations is tested where it is shown that those differences are range-dependent. The work fluctuation theorem corresponding to these entropies is also established. Small deviations in the decaying behavior of the average of the ratio of work probabilities are observed, and the expressions for the generalized work theorem consistently converge to zero.