Vibration-based condition monitoring and fault diagnosis is an effective approach to maintain the reliable operation of a scroll compressor. Unfortunately, the vibration signal from the scroll compressor always has characteristics of being non-linear and non-stationary, which makes vibration signal analysis and fault feature extraction very difficult. To extract the significant fault features, ...

in this paper we introduce the concept of entropy operator for continuous systems of finite topological entropy. it is shown that it generates the kolmogorov entropy as a special case. if $phi$ is invertible then the entropy operator is bounded with the topological entropy of $phi$ as its norm.

Quantum theory of geometry that has been developed recently in the framework of non-perturbative quantum gravity is used in an attempt to explain thermodynamics of Schwarzschild black hole on the basis of microscopical (quantum) description. We work with the formulation of thermodynamics in which black hole is enclosed by a spherical surface B and a macroscopic state of the system is speciied b...

A general framework is proposed for the derivation and analysis of ux-splittings and the corresponding ux-splitting schemes for systems of conservation laws endowed with a strictly convex entropy. The approach leads to several new properties of the existing ux-splittings and to a method for the construction of entropy ux-splittings for general situations. A large family of genuine entropy ux-sp...

The entanglement entropy is a fundamental quantity, which characterizes the correlations between sub-systems in a larger quantum-mechanical system. For two sub-systems separated by a surface the entanglement entropy is proportional to the area of the surface and depends on the UV cutoff, which regulates the short-distance correlations. The geometrical nature of entanglement-entropy calculation ...

We develop the argument that the Gibbs-von Neumann entropy is the appropriate statistical mechanical generalisation of the thermodynamic entropy, for macroscopic and microscopic systems , whether in thermal equilibrium or not, as a consequence of Hamiltonian dynamics. The mathematical treatment utilises well known results [Gib02, Tol38, Weh78, Par89], but most importantly, incorporates a variet...

We normalize the combinatorial Laplacian of a graph by the degree sum, look at its eigenvalues as a probability distribution and then study its Shannon entropy. Equivalently, we represent a graph with a quantum mechanical state and study its von Neumann entropy. At the graph-theoretic level, this quantity may be interpreted as a measure of regularity; it tends to be larger in relation to the nu...

We propose an extension of the principle of virtual work of mechanics to random dynamics of mechanical systems. The total virtual work of the interacting forces and inertial forces on every particle of the system is calculated by considering the motion of each particle. Then according to the principle of Lagrange-d’Alembert for dynamical equilibrium, the vanishing ensemble average of the virtua...

The change in entropy, S , associated with the quasi-static absorption of a particle of energy ε by a Schwarzschild black hole (ScBH) is approximately (ε/T )− s, where T is the Hawking temperature of the black hole and s is the entropy of the particle. Motivated by the statistical interpretation of entropy, it is proposed here that the absorption should be suppressed, but not forbidden, when S ...

For a dynamical system far from equilibrium, one has to deal with empirical probabilities defined through time–averages, and the main problem is then how to formulate an appropriate statistical thermodynamics. The common answer is that the standard functional expression of Boltzmann-Gibbs for the entropy should be used, the empirical probabilities being substituted for the Gibbs measure. Other ...