Related papers: Entropy formula of N-body system
After a brief introduction to the concept of entanglement in quantum systems, I apply these ideas to many-body systems and show that the von Neumann entropy is an effective way of characterising the entanglement between the degrees of…
This is a study of composition rule and temperature definition for nonextensive systems containing different $q$ subsystems. The physical meaning of the multiplier $\beta$ associated with the energy expectation in the optimization of…
The paper suggests the concepts of an upper entropy and a lower entropy. We propose a new axiomatic definition, namely, upper entropy axioms, inspired by axioms of metric spaces, and also formulate lower entropy axioms. We also develop weak…
We have discussed the validity of the factorization approximation (FA) and nonextensivity-induced correlation, by using the multivariate $q$-Gaussian probability distribution function (PDF) for $N$-unit independent nonextensive systems. The…
Using arguments built on ergodicity, we derive an analytical expression for the Renyi entanglement entropies corresponding to the finite-energy density eigenstates of chaotic many-body Hamiltonians. The expression is a universal function of…
The universal validity of the second law of thermodynamics is widely attributed to a finely tuned initial condition of the universe. This creates a problem: why is the universe atypical? We suggest that the problem is an artefact created by…
The equilibria formed by the self-gravitating, collisionless collapse of simple initial conditions have been investigated for decades. We present the results of our attempts to describe the equilibria formed in $N$-body simulations using…
In this research paper, it is proved that an approximation to Gibbs-Shannon entropy measure naturally leads to Tsallis entropy for the real parameter q =2 . Several interesting measures based on the input as well as output of a discrete…
The present article is concerned with the use of approximations in the calculation of the many-body density of states (MBDS) of a system with total energy E, composed by N bosons. In the mean-field framework, an integral expression for…
During the past dozen years there have been numerous articles on a relation between entropy and probability which is non-additive and has a parameter $q$ that depends on the nature of the thermodynamic system under consideration. For $q=1$…
Boltzmann's principle S(E,N,V...)=ln W(E,N,V...) allows the interpretation of Statistical Mechanics of a closed system as Pseudo-Riemannian geometry in the space of the conserved parameters E,N,V... (the conserved mechanical parameters in…
We investigate the behavior of the Gibbs-Shannon entropy of the stationary nonequilibrium measure describing a one-dimensional lattice gas, of L sites, with symmetric exclusion dynamics and in contact with particle reservoirs at different…
In the works on Statistical Mechanics and Statistical Physics, when deriving the distribution of particles of ideal gases, one uses the method of Lagrange multipliers in a formal way. In this paper we treat rigorously this problem for…
The homogeneous entropy for continuous systems in nonextensive statistics reads $S^{H}_{q}=k_B\,{(1 - (K \int d\Gamma \rho^{1/q}(\Gamma))^{q})}/({1-q})$, where $\Gamma$ is the phase space variable. Optimization of $S^{H}_{q}$ combined with…
Using the lattice QCD equation of state for an isentropically expanding fireball we follow the evolution of the effective number of particles in an ideal gas pV/T. This number reduces roughly to its third around the crossover temperature,…
We study non-equilibrium quantum dynamics of the single-component scalar field theory in 1+1 space-time dimensions on the basis of the Kadanoff-Baym equation including the next-to-leading-order (NLO) skeleton diagrams. As an extension of…
As first shown by H. S. Green in 1952, the entropy of a classical fluid of identical particles can be written as a sum of many-particle contributions, each of them being a distinctive functional of all spatial distribution functions up to a…
The science of thermodynamics was put together in the Nineteenth Century to describe large systems in equilibrium. One part of thermodynamics defines entropy for equilibrium systems and demands an ever-increasing entropy for non-equilibrium…
Microscopic formula to describe the entropy of biomolecular solutions are derived based on the Gibbs formula of entropy, and the generalized Langevin theory combined with the RISM/3D-RISM theory. Two formula are derived: one is concerned…
Some general considerations on the notion of entropy in physics are presented. An attempt is made to clarify the question of the differentiation between physical entropy (the Clausius-Boltzmann one) and quantities called entropies…