We develop the stochastic approach to thermodynamics based on stochastic dynamics, which can be discrete (master equation) and continuous (Fokker-Planck equation), and on two assumptions concerning entropy. The first is the definition of entropy itself and the second the definition of entropy production rate, which is non-negative and vanishes in thermodynamic equilibrium. Based on these assump...

The purpose of this study is to define the concepts of Tsallis entropy and conditional Tsallis entropy of fuzzy partitions and to obtain some results concerning this kind entropy. We show that the Tsallis entropy of fuzzy partitions has the subadditivity and concavity properties. We study this information measure under the refinement and zero mode subset relations. We check the chain rules for ...

A class of non-equilibrium models for compressible multi-component fluids in multi-dimensions is investigated taking into account viscosity and heat conduction. These models are subject to the choice of interfacial pressures and interfacial velocity as well as relaxation terms for velocity, pressure, temperature and chemical potentials. Sufficient conditions are derived for these quantities tha...

We show that it is impossible to compute (or even to approximate) the topological entropy of a continuous piecewise affine function in dimension four. The same result holds for saturated linear functions in unbounded dimension. We ask whether the topological entropy of a piecewise affine function is always a computable real number, and conversely whether every non-negative computable real numbe...

The quantum entropy of the Kerr black hole arising from gravitational perturbation is investigated by using Null tetrad and ’t Hooft brick-wall model. It is shown that the effect of the graviton’s spin to the entropy is dependent of the square of the spin and the angular momentum per unit mass of the black hole, and contribution of logarithm term to the entropy will be positive, zero, and negat...

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...

Based on the form invariance of the structures given by Khinchin’s axiomatic foundations of information theory and the pseudoadditivity of the Tsallis entropy indexed by q , the concept of conditional entropy is generalized to the case of nonadditive (nonextensive) composite systems. The proposed nonadditive conditional entropy is classically nonnegative but can be negative in the quantum conte...

We report results of specific heat measurements from 5 to 70 K on thin films of the giant negative magnetoresistive spin glass a-GdxSi12x and its nonmagnetic analog a-YxSi12x . The specific heat of a-GdxSi12x samples is significantly greater than that of a-YxSi12x samples below 50 K. The resulting magnetic entropy of a-GdxSi12x exceeds the total calculated entropy available from Gd moments alon...

An information theoretic framework for grouping observations is proposed. The entropy change incurred by new observations is analyzed using the Kalman filter update equations. It is found, that the entropy variation is caused by a positive similarity term and a negative proximity term. Bounding the similarity term in the spirit of the minimum description length principle and the proximity term ...

An information theoretic approach is used to hide a visually meaningful and recognizable two level watermark symbol in the spatial domain. Watermark insertion regions are selected using both Shannon’s entropy measure as well as non-Shannonian entropy for image data. Experimental results confirm the robustness of the proposed scheme against several kinds of attacks, such as lossy compression, fi...