The theoretical limits of ’lossy’ data compression algorithms are considered. The complexity of an object as seen by a macroscopic observer is the size of the perceptual code which discards all information that can be lost without altering the perception of the specified observer. The complexity of this macroscopically observed state is the simplest description of any microstate comprising that...

In this Contribution we show that a suitably defined nonequilibrium entropy of an N-body isolated system is not a constant of the motion, in general, and its variation is bounded, the bounds determined by the thermodynamic entropy, i.e., the equilibrium entropy. We define the nonequilibrium entropy as a convex functional of the set of n-particle reduced distribution functions n N generalizing t...

Hawking radiation is viewed as a tunnelling process. In this way the effect of selfgravitation gives rise to quantum corrections to the entropy of the (2+1) BTZ black hole. The modified entropy, due to specific modelling of the self-gravitation effect, of the (2+1) BTZ black hole is evaluated. To first order in ω which is a shell of energy radiated outwards the event horizon of the BTZ black ho...

In this work, we extend a variable-length source coding theorem for discrete memoryless sources to ergodic time-invariant Markov sources of arbitrary order. To accomplish this extension, we establish a formula for the R enyi entropy rate lim n!1 H (n)=n. The main tool used to obtain the R enyi entropy rate result is Perron-Frobenius theory. We also examine the expression of the R enyi entropy r...

We review some results on the connection among supergravity central charges, BPS states and Bekenstein{Hawking entropy. In particular, N = 2 supergravity in four dimensions is studied in detail. For higher N supergravities we just give an account of the general theory specializing the discussion to the N = 8 case when one half of supersymmetry is preserved. We stress the fact that for extremal ...

The Cardy-Verlinde formula is further verified by using the Kerr-NewmanAdS4 and Kerr-Newman-dS4 black holes. In the Kerr-Newman-AdS4 spacetime, we find that, for strongly coupled CFTs with AdS duals, to cast the entropy of the CFT into the Cardy-Verlinde formula the Casimir energy must contains the terms −n ( JΩH + QΦ 2 + QΦ0 2 ) , which associate with rotational and electric potential energies...

We develop the general, multivariate case of the Edgeworth approximation of differential entropy, and introduce an approximate formula for Gaussian mixture densities. We use these entropy approximations in a new algorithm for selecting the optimal number of clusters in a data set, and in a new mutual information test with which one can statistically decide whether a distribution can be factoriz...

We argue that the statistical entropy relevant for the thermal interactions of a black hole with its surroundings is (the logarithm of) the number of quantum microstates of the hole which are distinguishable from the hole's exterior, and which correspond to a given hole's macroscopic conguration. We compute this number explicitly from rst principles, for a Schwarzschild black hole, using nonper...

We present evidence which con rms a suggestion by Susskind and Uglum regarding black hole entropy. Using a Pauli-Villars regulator, we nd that 't Hooft's approach to evaluating black hole entropy through a statistical-mechanical counting of states for a scalar eld propagating outside the event horizon yields precisely the one-loop renormalization of the standard Bekenstein-Hawking formula, S = ...

The standard approach of counting the number of eigenmodes of N scalar fields near the horizon is used as a basis to provide a simple statistical mechanical derivation of the black hole entropy in two and four dimensions. The Bekenstein formula S = A 4Gh̄ and the two-dimensional entropy S = 2M/λh̄ are naturally obtained (up to a numerical constant of order 1). This approach provides an explanatio...