Related papers: Valiron-Titchmarsh Theorem for Positive Temperatur…

We give a proof of the Marker-Steinhorn Theorem which fills a gap in previous proofs of the result.

Using the integral representations of the solutions of Schr\"odinger equation, which are the essential ingredients of the Gel'fand-Levitan and Marchenko integral equations of inverse scattering theory, we obtain a general theorem on the…

We prove a conjecture of Dale Peterson on positivity in the multiplication in the T-equivariant cohomology of the flag variety. The theorem follows from a more general positivity result about the equivariant cohomology of varieties with…

The equipartition theorem is a fundamental law of classical statistical physics, which states that every degree of freedom contributes $k_{B}T/2$ to the energy, where $T$ is the temperature and $k_{B}$ is the Boltzmann constant. Recent…

Providing students of introductory thermal physics with a plot of the heat capacities of many low density gases as a function of temperature allows them to look for systematic trends. Specifically, large amounts of heat capacity data allow…

A first order phase transition leading to deconfinement and chiral restoration is a likely possibility for QCD, at least in some region of the temperature-density plane. A signal for a unique transition is that the order parameters for such…

We give a simple and intuitive proof that the only states which are completely passive, i.e. those states from which work cannot be extracted even with infinitely many copies, are Gibbs states at positive temperatures. The proof makes use…

The Bollob\'as-Varopoulos theorem is an analogue of Hall's matching theorem on non-atomic measure spaces. Here we prove a finite version with a completely constructive proof.

Within the context of a linear theory of heat-flux dependent thermoelasticity for micropolar porous media some variational principles and a reciprocal relation are derived.

We state and prove a version of Dyson's Lemma for a product of smooth projective varieties of arbitrary dimension using positivity methods.

A multivariate Gauss-Lucas theorem is proved, sharpening and generalizing previous results on this topic. The theorem is stated in terms of a seemingly new notion of convexity. Applications to multivariate stable polynomials are given.

The Thermal Time Hypotheis (TTH) has been proposed as a general method for identifying a time variable from within background-free theories which do not come equipped with a pre-defined clock variable. Here, we explore some implications of…

In this paper, we will prove a zero comparison theorem of Sturm-Liouville type for linearized harmonic heat flow for rotational symmetric solutions.

The purpose of this letter is to point out an argument which may ultimately lead to a rigorous proof of the Penrose inequality in the general case. The argument is a variation of Geroch's original proposal for a proof of the positive energy…

We present some necessary and/or sufficient conditions for the positivity problem of three-term recurrence sequences. As applications we show the positivity of diagonal Taylor coefficients of some rational functions in a unified approach.…

We give an interpretation to the issue of the chiral determinant in the heat-kernel approach. The extra dimension (5-th dimension) is interpreted as (inverse) temperature. The 1+4 dim Dirac equation is naturally derived by the Wick rotation…

One considers the motion of a test particle in an homogeneous fluid in equilibrium at temperature $T$, undergoing dissipative collisions with the fluid particles. It is shown that the corresponding linear Boltzmann equation still posseses a…

We show that thermalization of the motion of atoms at negative temperature is possible in an optical lattice, for conditions that are feasible in current experiments. We present a method for reversibly inverting the temperature of a trapped…

Given the full shift over a countable state space on a countable amenable group, we develop its thermodynamic formalism. First, we introduce the concept of pressure and, using tiling techniques, prove its existence and further properties…

Starting from the Lifshitz formula for the Casimir force between parallel plates we calculate the difference between the forces at two different settings, one in which the temperature is $T_1=350$ K, the other when $T_2=300$ K. As material…