Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userConditional entropy; an alternative derivation of the pair correlation function for simple classical fluids
75
0
0.0
(
0
)
Authors
Richard Bonneville
Ask ChatGPT about the research
No Arabic abstract
We present an alternative derivation of the pair correlation function for simple classical fluids by using a variational approach. That approach involves the conditional probability p(3,..., N /1, 2) of an undefined system of N particles with respect to a given pair (1,2), and the definition of a conditional entropy $sigma$(3,..., N /1, 2). An additivity assumption of $sigma$(3,..., N /1, 2) together with a superposition assumption for p(3 / 1, 2) allows deriving the pair probability p(1,2). We then focus onto the case of simple classical fluids, which leads to an integral, non-linear equation that formally allows computing the pair correlation function g(R). That equation admits the one resulting from the hyper netted chain approximation (and the Percus-Yevick approximation) as a limit case.
rate research
Read More
The original perturbative Kramers method (starting from the phase space coordinates) (Kramers, 1940) of determining the energy-controlled-diffusion equation for Newtonian particles with separable and additive Hamiltonians is generalized to yield the energy-controlled diffusion equation and thus the very low damping (VLD) escape rate including spin-transfer torque for classical giant magnetic spins with two degrees of freedom. These have dynamics governed by the magnetic Langevin and Fokker-Planck equations and thus are generally based on non-separable and non-additive Hamiltonians. The derivation of the VLD escape rate directly from the (magnetic) Fokker-Planck equation for the surface distribution of magnetization orientations in the configuration space of the polar and azimuthal angles $(vartheta, varphi)$ is much simpler than those previously used.
We report on recent results that show that the pair correlation function of systems with exponentially decaying interactions can fail to exhibit Ornstein-Zernike asymptotics at all sufficiently high temperatures and all sufficiently small densities. This turns out to be related to a lack of analyticity of the correlation length as a function of temperature and/or density and even occurs for one-dimensional systems.
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 given order. By revisiting the combinatorial derivation of the entropy formula, we argue that a similar correlation expansion holds for the entropy of a crystalline system. We discuss how one- and two-body entropies scale with the size of the crystal, and provide fresh numerical data to check the expectation, grounded on theoretical arguments, that both entropies are extensive quantities.
A simple ansatz for the study of velocity autocorrelation functions in fluids at different timescales is proposed. The ansatz is based on an effective summation of the infinite continued fraction at a reasonable assumption about convergence of relaxation times of the higher order memory functions, which have a purely kinetic origin. The VAFs obtained within our approach are compared with the results of the Markovian approximation for memory kernels. It is shown that although in the overdamped regime both approaches agree to a large extent at the initial and intermediate times of the system evolution, our formalism yields power law relaxation of the VAFs which is not observed at the description with a finite number of the collective modes. Explicit expressions for the transition times from kinetic to hydrodynamic regimes are obtained from the analysis of the singularities of spectral functions in the complex frequency plane.
Pressure is the mechanical force per unit area that a confined system exerts on its container. In thermal equilibrium, it depends only on bulk properties (density, temperature, etc.) through an equation of state. Here we show that in a wide class of active systems the pressure depends on the precise interactions between the active particles and the confining walls. In general, therefore, active fluids have no equation of state, their mechanical pressures exhibit anomalous properties that defy the familiar thermodynamic reasoning that holds in equilibrium. The pressure remains a function of state, however, in some specific and well-studied active models that tacitly restrict the character of the particle-wall and/or particle-particle interactions.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
