The result is compared with the Bekenstein formula for entropy bound, which was initially derived from the generalized second law of thermodynamics for black holes. The holographic principle states that the ent
At zero temperature we reproduce a logarithmic formula of Holzhey, Larsen and Wilczek. Our derivation is based on the second law of thermodynamics. The entropy of a subsystem is calculated explicitly for Bose gas with delta interaction, the Hubbard model and spin chains with arbitrary value of ...
The formulae given above for entropy and probability are surprisingly powerful, despite their evident simplicity and that of their derivation. All of thermodynamics and statistical mechanics is based upon these results and the notions that underlie them. Show moreView chapter Chapter Isolated Systems an...
Through this formula, Boltzmann first calculates the entropy of a monoatomic gas and then that of a system of independent oscillators, respectively, finding the first consistent with that derivable from standard thermodynamics, and using the second to work out the Dulong–Petit law for the heat ...
Thermodynamics is an empirical physical theory which describes relevant aspects of the behavior of macroscopic systems. In some form or another, all large physical systems are shown to satisfy this theory. It is based on two most relevant concepts, namely energy and entropy. The German physicist ...
Ex1 produces an infinite number of strings s, s∈ Σ*, each of which corresponds to a unique derivation or parsing. Being exclusive events, the sum of all possible derivations converges to one in the limit of infinity, ∑i=0∞αβi=1, while the expected word length converges to the ...
in the Jarzynski equality and fluctuation relations and other tools of stochastic thermodynamics, using large deviation theory or others. When recognized as an inference principle, entropy maximization can be generalized for non-equilibria and applied to path entropies rather than state entropies, becomi...
The foundation of black hole thermodynamics was laid in the 1970s through the pioneering work of Jacob Bekenstein and Stephen Hawking. Bekenstein proposed that the entropy of a black hole is proportional to the area of its event horizon, not its volume—an insight that fundamentally shifted our ...
In particular, the thermodynamics of the Schwarzschild black hole of radius R has the form M= R, 2G T = 1 4π R , S= A , 4G (1) where we have set h¯ = c = K B = 1. The celebrated Bekenstein–Hawking entropy A 4G is often called holographic entropy because of its ...
It is important to note that the derivation of black hole entropy by Iyer and Wald [7, 8, 23], consistent with the first law of thermodynamics, and all the subsequent developments mentioned above in [10, 18, 19, 21], are based on Noether formalism which heavily relies on diffeomorphism ...