arXiv subjects

P. B. Krishna

Publications and source records attributed to P. B. Krishna.

5 recordsLinked to original sources

arXiv2026

Horizon energy fluctuations beyond Einstein's gravity: Gauss-Bonnet, Lovelock and Quantum deformed frameworks

We study thermal energy fluctuations of cosmological horizons within the canonical ensemble framework, treating the horizon as a thermodynamic system characterized by temperature and entropy. The analysis is performed for a class of gravitational theories, including (n+1)-dimensional Einstein gravity, Gauss-Bonnet gravity, Lovelock gravity, and models incorporating quantum deformed entropy corrections. We find that horizon energy fluctuations stabilize to a constant value in the asymptotic de Sitter limit, independent of the underlying gravity theory and robust against higher-curvature and quantum corrections. It is worth mentioning that in its final de Sitter state, the universe obeys holographic equipartition condition and in consequence the horizon entropy attains a maximum constant value, just like an ordinary macroscopic system. These findings establish a unified thermodynamic picture in which entropy maximization, holographic equipartition, and the suppression of energy fluctuations collectively characterize the asymptotic de Sitter universe as the equilibrium end state of cosmic evolution.

gr-qc↗

arXiv2023

Unified formalism for the emergence of space from the first law of thermodynamics

We derive a unified expansion law for our universe from the first law of thermodynamics on the apparent horizon, where entropic evolution depicts the emergence of cosmic space. The derivation advances a general form for degrees of freedom on the surface and bulk, which provides a natural generalization for the expansion law proposed by Padmanabhan. The general expression for the surface degrees of freedom differs from the natural expectation, $ N_{sur }= 4S $ in the emergent gravity paradigm for general theories of gravity. The derivation also provides justification for the selection of Gibbons-Hawking temperature in the original expansion law and for the use of areal volume in the non-flat FRW universe. Since the unified expansion law exclusively depends on the form of entropy, the method is applicable to obtain the expansion law in any gravity theory without any additional ad hoc assumptions. From the general expansion law, we have obtained the expansion law corresponding to different theories of gravity like (n+1) Einstein, Gauss-Bonnet, Lovelock, and Horava-Lifshitz. We also obtained the expansion law for non-extensive entropy like Tsallis entropy from the unified expansion law.

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arXiv2022

Emergence of cosmic space and its connection with thermodynamic principles

The recent research on the connection between gravity and thermodynamics suggests that gravity could be an emergent phenomenon. Following this, Padmanabhan proposed a novel idea that the expansion of the universe can be interpreted as equivalent to the emergence of space with the progress of cosmic time. In this approach, the expansion of the universe is described by what is known as the law of emergence, which states that the expansion of the universe is driven by the difference between the number of bulk and surface degrees of freedom in a region bounded by the Hubble radius. This principle correctly reproduces the standard evolution of a Friedmann universe. We establish the connection of the law of emergence, which is conceptually different from the conventional paradigm to describe cosmology, with other well-established results in thermodynamics. It has been shown that the law of emergence can be derived from the unified first law of thermodynamics, which can then be considered as the backbone of the law. However, the law of emergence is rich in structure than implied by the First law thermodynamics alone. It further explains the evolution of the universe towards a state of maximum horizon entropy. Following this, it can be considered that the first law of thermodynamics, along with the additional constraints imposed by the maximisation of the horizon entropy, can together lead to the law of emergence. In the present article, we first make a brief review of Padmanabhan's proposal and then studies its connection with the thermodynamics of the horizon in the context of Einstein's, Gauss-Bonnet, and more general Lovelock gravity theories.

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arXiv2021

Emergence of space from non-equilibrium thermodynamics in f(R) gravity

It has shown that the accelerated expansion of the FRW Universe can be explained as the quest towards the holographic equipartition ($N_{sur} = N_{bulk}$), satisfies the expansion law $\frac{dV}{dt} = l_{P}^{2} \left( N_{sur} - εN_{bulk} \right)$, from which one can derive the Friedmann equation of the FRW Universe in Einstein gravity \cite{paddy2012jun}. We introduce a generic derivation of the expansion law from the generalized first law of thermodynamics $-dE=TdS$ and $dE=TdS + WdV$. The generic derivation provides an expression for $N_{sur}$ in terms of entropy $S$ and the expansion law consistent with gravity theories having different entropy $S$, like Gauss-Bonnet and more general Lovelock gravity. We extended the same idea to the non-equilibrium situation and obtained the expansion law in f(R) gravity as a specific case. For this, we used the first law of thermodynamics in non-equilibrium description having the extra entropy production term $Td_{i}S.$

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arXiv2019

First Law of Thermodynamics and Emergence of Cosmic Space in a Non-Flat Universe

The emergence of cosmic space as cosmic time progresses is an exciting idea advanced by Padmanabhan to explain the accelerated expansion of the universe. The generalization of Padmanabhan's conjecture to the non-flat universe has resulted in scepticism about the choice of volume such that the law of emergence can not be appropriately formulated if one uses proper invariant volume. The deep connection between the first law of thermodynamics and the law of emergence \cite{mahith}, motivate us to explore the status of the first law in a non-flat universe when one uses proper invariant volume. We have shown that the first law of thermodynamics, $dE = TdS +WdV$ cannot be formulated properly for a non-flat universe using proper invariant volume. We have also investigated the status of the first law of the form $-dE = TdS$ in a non-flat universe. We have shown that the energy change dE within the horizon and the outward energy flux are not equivalent to each other in a non-flat universe when we use the proper invariant volume. We have further shown that the consistency between the above two forms of the first law claimed in Ref. \cite{caiakb} will hold only with the use of the areal volume of the horizon. Thus, a consistent formulation of the above two forms of the first law of thermodynamics demands the use of areal volume.

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