arXiv subjects

Amijit Bhattacharjee

Publications and source records attributed to Amijit Bhattacharjee.

6 recordsLinked to original sources

arXiv2026

Information-Geometric Signatures from Nonextensivity in the $1$-D Blume-Capel Model

We study the thermodynamic geometry of the one-dimensional Blume--Capel model within the Tsallis nonextensive framework to understand how generalized statistics modify correlation structure and pseudo-critical behaviour. Using the transfer matrix method, we construct the Tsallis entropy based thermodynamic metric as its negative Hessian on the parameter space $(\beta, J)$, with the crystal-field anisotropy $D$ as a control parameter, and compute the associated scalar curvature $R(T)$ as a measure of correlations. Although no true phase transition occurs in one dimension, $R(T)$ exhibits finite peaks signaling pseudo-critical crossovers. We analyze both $D < J$ and $D > J$ regimes and show that deviations from the Boltzmann--Gibbs limit ($q=1$) systematically deform the curvature profile: for $q>1$ the peak shifts and correlations persist beyond the crossover, whereas for $q<1$ the peak is weakened or suppressed. Our results demonstrate that the Tsallis parameter $q$ geometrically reshapes the entropy surface, providing a clear information-geometric interpretation of nonextensive effects in spin-1 systems.

cond-mat.stat-mech↗

arXiv2026

Testing the AdS/CFT Correspondence Through Thermodynamic Geometry of Nonlinear Electrodynamics AdS Black Holes with Generalized Entropies

We investigate the thermodynamics and thermodynamic geometry of several Anti--de Sitter black hole solutions arising from nonlinear electromagnetic theories, namely the ModMax, nonlinear electrodynamics (NED), and Euler--Heisenberg AdS black holes, together with their holographically dual conformal field theory (CFT) descriptions. The analysis is carried out within three entropy frameworks: the standard Bekenstein--Hawking entropy and the generalized R\'enyi and Kaniadakis entropies. For each system, we analyze the phase structure through the behavior of temperature, specific heat, and the scalar curvature obtained from geometrothermodynamics (GTD). We find that thermodynamic critical points correspond to extrema in the temperature--entropy relation and coincide with divergences of the specific heat. These locations are reproduced by singularities in the Legendre--invariant GTD curvature, demonstrating a consistent geometric interpretation of the phase transitions. A comparison between the bulk black hole systems and their dual CFT counterparts shows that the number and structure of critical points are preserved under the holographic correspondence. Our results further reveal that the Euler--Heisenberg AdS black hole exhibits a more intricate phase structure compared with the ModMax and NED cases, while the Kaniadakis entropy consistently generates an additional critical point across all systems considered. These findings highlight the combined influence of nonlinear electromagnetic dynamics and generalized entropy formalisms on the critical behavior of AdS black holes and their dual CFTs.

hep-th↗

arXiv2025

Restricted Phase Space Thermodynamics of Charged Static and Charged Rotating Black Holes in $f(R)$ Gravity

The thermodynamics of black holes provides a profound link between gravity, quantum theory and statistical mechanics. It serves as a useful tool for testing theories beyond Einstein's gravity. In this work of ours, we investigate the newly found restricted phase space thermodynamics (RPST) of charged static and charged rotating black holes in $f(R)$ gravity. Unlike the extended phase space (EPST) approach, RPST keeps the cosmological constant fixed and introduces the central charge $C$ along with its conjugate chemical potential $\mu$, thereby allowing the black hole mass to be consistently interpreted as internal energy. Within this framework, we derive the relevant thermodynamic quantities and analyse the temperature-entropy $(T-S)$ and Helmholtz free energy-temperature $(F-T)$ behaviours. Our results reveal characteristic features of first-order phase transitions through non-monotonic $T-S$ curves along with the swallow-tail structures in $F-T$ plots, while second-order transitions appear at critical points. To further validate these findings, we employ the formalism of geometrothermodynamics (GTD), which provides a Legendre-invariant geometric description of thermodynamic geometry. We demonstrate that the curvature singularities of the GTD scalar curvature coincides exactly with that of the divergences in the specific heat capacity curves, thereby establishing a geometric correspondence for phase transitions. This study facilitates the first systematic exploration of RPST within $f(R)$ gravity and highlights the universality of RPST in capturing black hole criticality in modified gravity theories.

hep-th↗

arXiv2025

Thermodynamics of Flat 4D Einstein-Gauss-Bonnet Black Hole with R\'enyi Entropy: An RPST-like formalism

We investigate the thermodynamics of asymptotically flat black holes in four-dimensional Einstein-Gauss-Bonnet (4D-EGB) gravity using R\'enyi entropy as a non-extensive generalization of the Bekenstein-Hawking entropy. The resulting thermodynamic structure, formulated within a restricted phase space-like (RPST-like) framework, reveals a striking resemblance to the thermodynamics of AdS black holes in the standard RPST formalism. In particular, we identify a thermodynamic duality between the R\'enyi deformation parameter $\beta$ and a conjugate response potential $\zeta$, analogous to the central charge and chemical potential in holographic theories. An extensive thermodynamic analysis in both fixed charge-$(\tilde{Q})$ and fixed potential-$(\tilde{\Phi})$ ensembles reveal Van der Waals-like first-order phase transitions which is an unexpected feature for asymptotically flat black holes. Furthermore, through the formalism of geometrothermodynamics (GTD) and thermodynamic topology, It is shown that the R\'enyi modified flat black hole mimics, in both its thermodynamic topology and geometry, the features of its counterparts in the 4D-EGB AdS black hole under RPST, reinforcing the structural similarity between these seemingly different systems. Our findings point to a deeper correspondence between non-extensive entropy and holographic thermodynamics, suggesting that R\'enyi entropy may serve as a natural bridge between flat-space black hole thermodynamics and AdS holography.

hep-th↗

arXiv2024

BTZ Black Hole In The Non-Extensive Generalizations of Gibbs Entropy

We study the thermodynamics and thermodynamic geometry of the (2+1) dimensional Banados-Teitelboim-Zanelli(BTZ) black hole within the framework of the non-extensive generalizations of Gibbs entropy. We investigate both the rotating (R-BTZ) and the charged (C-BTZ) BTZ black holes in these non-extensive entropy formalisms. We write down the Bekenstein-Hawking(BH) entropy of the black hole in terms of the non-extensive entropies namely: Kaniadakis entropy, Renyi entropy and Barrow entropy. We investigate their impact on the thermodynamic phase structure and geometry of the BTZ black holes in both the ensembles i.e. the fixed $(J)$ and fixed $(\Omega)$ ensemble for the R-BTZ black hole and the fixed $(Q)$ and the fixed $(\Phi)$ ensemble for the C-BTZ black hole where $ J$, $\Omega$, $Q$ and $\Phi$ represent the angular momentum, angular velocity, charge and the electric potential of the respective black holes . We investigate the Ruppeiner and geometrothermodynamic(GTD) geometries of the black hole for all the non-extensive entropy cases. We find that there are Davies type along with Hawking-Page phase transitions in both the charged and rotating BTZ black hole for the Kaniadakis entropy case in all the above mentioned thermodynamic ensembles. These phase transitions were not seen in the BH entropy case. We also find that the Ruppeiner and the GTD scalar for the Kaniadakis entropy show curvature singularities corresponding to the Davies type phase transitions in both the rotating and charged BTZ black holes.

hep-th↗

arXiv2024

Thermodynamics of Rotating AdS black holes in Kaniadakis statistics

In this study, we advance the understanding of thermodynamic properties and phase transitions in rotating anti-de Sitter (AdS) black holes by applying the Kaniadakis(KD) entropy framework. This framework represents a non-extensive generalization of classical statistical mechanics, inspired by the symmetries of relativity and offering a novel perspective on black hole thermodynamics. Our focus is on investigating how Kaniadakis entropy modifies the thermodynamic phase space of rotating AdS black holes. To achieve this, we analyze three prominent rotating AdS black hole systems: the Kerr AdS black hole, the Kerr-Sen AdS black hole, and the Kerr-Newman AdS black hole. We assess their thermodynamic quantities, phase transitions, thermodynamic topology and thermodynamic geometry within the Kaniadakis statistical framework. Our analysis reveals notable deviations from the behaviour predicted by traditional Gibbs-Boltzmann(GB) statistics.

gr-qc↗