Search Results

The Loschmidt paradox is valid only in bounded systems with finitely many degrees of freedom, as the proof of Poincare recurrence fails in an unbounded domain, or if the number of degrees of freedom i …

There is no single point where this becomes true - it is a very gradual change. The buzzwords are microscopic $\to$ mesoscopic $\to$ macroscopic. There is no special kind of mathematics involved; in …

Considerations like those you mention are just informal, intuitive illustrations, not stringent derivations. They anyway apply only to the simplest situations - ideal gases. Landau and Lifshitz (and w …

The assumption of a full eigensystem is usually made for convenience. But it is not always satisfied. If it is not satisfies one gets additional logarithmic contributions to the scaling laws. This is …

It is just what is needed to describe a pure chemical substance. For other systems you may have fewer or more than 3 degrees of freedom - yes, many dof may occur in practice, think of a complex mixtur …

For a system in thermal equilibrium, the only admissible macrostates are those of the form $\rho=e^{-S/k_B}$, where $S$ is a linear combination of additively conserved quantum numbers. This severly li …

The precise relation is given by $f(q,p,t)=\int \rho(q^N,p^N,t)\delta(q-Q)\delta(p-P)dq^Ndp^N$, where $Q$ is the center of mass of $q^N=(q_1,\ldots,q_N)$, and $P$ is the total momentum, the sum of $p …

For a rigorous derivation of statistical mechanics from quantum mechanics see Chapters 8-10 of my book: Classical and Quantum Mechanics via Lie algebras http://lanl.arxiv.org/abs/0810.1019

Negative temparature makes sense in statistical mechanics only if the associated Hamiltonian is bounded from above; otherwise the trace in the definition of the partition function does not exist. In …

The question can be answered most easily by considering a grand canonical ensemble, where the density operator has the form $\rho=Z^{-1}e^{-\beta(H-\mu N)}$, with $\beta=1/kT$ where $k$ is Boltzmann's …

It is explained on the first page of http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1076959/pdf/pnas01784-0023.pdf ''If E is any invariant measurable set, then either E or its complement is of measure …

A perturbation is a small change (usually deterministic and known), while a fluctuation is a (not necessarily small) random perturbation with mean zero (and therefore either unknown or unrepeatable). …

The main criticism: The maximum entropy principle works (i.e., gives a correct description of a physically system) if and only if the knowledge of the observer is of a very special kind, namely con …

Part II of my online book A. Neumaier and D. Westra, Classical and Quantum Mechanics via Lie algebras (2011 version) does precisely that. While it starts off with a chapter giving an axiomatic treatme …

Is this what you are looking for? All valid statements in the equilibrium thermodynamics of standard systems can be deduced from the following definition. 7.1.2 Definition. (Phenomenological thermody …