We present an efficient sampling method for computing a partition function and accelerating configuration sampling. The method performs a random walk in the lambda space, with lambda being any thermodynamic variable that characterizes a canonical ensemble such as the reciprocal temperature beta or any variable that the Hamiltonian depends on. The partition function is determined by minimizing t...

We derive the microcanonical partition function of the ideal relativistic quantum gas with fixed intrinsic angular momentum as an expansion over fixed multiplicities. We developed a group theoretical approach by generalizing known projection techniques to the Poincaré group. Our calculation is carried out in a quantum field framework and applies to particles with any spin. It extends known resu...

We consider a statistical mechanics of rotating ideal gas consisting classical non-relativistic spinning particles. The microscopic structure elements the system are massive point particles with nonzero proper angular momentum. norm momentum is determined by spin. direction changes continuously. Applying Gibbs canonical formalism for system, we construct one-particle distribution function, gene...

We have used a toy model to study the behaviour of confined binary systems in 2D and compare it with previously known result in 3D. In the case of 2D, in which canonical distribution exists only above a critical temperature, we evaluate the exact form of partition function for this system and compare the exact partition function with the mean field partition function for the case of two-particl...

Recently it was shown[1] that the imaginary part of the canonical partition function of Schwarzschild black holes with an energy spectrum En = σ √ nEP , n = 1, 2, . . . , has properties which naively interpreted leads to the expected unusual thermodynamical properties of such black holes (Hawking temperature, Bekenstein-Hawking entropy etc.). The present paper interprets the same imaginary part...

In statistical mechanics, the canonical partition function [Formula: see text] can be used to compute equilibrium properties of a physical system. Calculating [Formula: see text] however, is in general computationally intractable, since the computation scales exponentially with the number of particles [Formula: see text] in the system. A commonly used method for approximating equilibrium proper...

By the theory of Eisenstein series, generating functions various divisor arise as modular forms. It is natural to ask whether further systematically in mock We establish, using method Zagier and Zwegers on holomorphic projection, that this indeed case for certain (twisted) “small divisors” summatory [Formula: see text]. More precisely, terms weight 2 quasimodular series text] a generic Shimura ...

We consider the Hamiltonian dynamics and thermodynamics of spherically symmetric spacetimes within a one-parameter family of five-dimensional Lovelock theories. We adopt boundary conditions that make every classical solution part of a black hole exterior, with the spacelike hypersurfaces extending from the horizon bifurcation three-sphere to a timelike boundary with fixed intrinsic metric. The ...

We calculate the density of states of the 2+1 dimensional BTZ black hole in the microand grand-canonical ensembles. Our starting point is the relation between 2+1 dimensional quantum gravity and quantised Chern-Simons theory. In the microcanonical ensemble, we find the Bekenstein–Hawking entropy by relating a Kac-Moody algebra of global gauge charges to a Virasoro algebra with a classical centr...