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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.
We derive the multiparticle-correlation expansion of the excess entropy of classical particles in the canonical ensemble using a new approach that elucidates the rationale behind each term in the expansion. This formula provides the theoretical frame
To illustrate Boltzmanns construction of an entropy function that is defined for a single microstate of a system, we present here the simple example of the free expansion of a one dimensional gas of hard point particles. The construction requires one
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
Conventional methods to calculate the thermodynamics of crystals evaluate the harmonic phonon spectra and therefore do not work in frequent and important situations where the crystal structure is unstable in the harmonic approximation, such as the bo
Recently, an Enskog-type kinetic theory for Vicsek-type models for self-propelled particles has been proposed [T. Ihle, Phys. Rev. E 83, 030901 (2011)]. This theory is based on an exact equation for a Markov chain in phase space and is not limited to