On the Sign of Local Temperature in Molecules

István Kolossváry

doi:10.3390/e1010004

Abstract

Lin proposed earlier based on qualitative considerations that electronic motion was associated with negative absolute temperature. Here, a local temperature formula is proposed for electronic motion in atoms and molecules, which allows the existence of negative absolute temperature in a local sense in thermodynamic equilibrium. The proposed temperature formula is a function of total energy density ε(r), entropy density s(r) and electron density ρ(r).

Highlights

What is heat? — A paramount question of thermodynamics is echoed in the title of Dyson’s popular paper some forty-five years ago [1]
The nuclear spin has only two states which means that a finite number of nuclear spins have a minimum energy state with all the spins being parallel to an external magnetic field, and, a maximum energy state with all the spins pointing in the opposite direction
According to eq 1 the maximum entropy state corresponds to infinite temperature, states toward the minimum energy state are in the positive temperature range, and states toward the maximum energy state are in the negative temperature range

Summary

Introduction

What is heat? — A paramount question of thermodynamics is echoed in the title of Dyson’s popular paper some forty-five years ago [1]. Quantitative analysis of this definition gives rise to the well-known thermodynamic relation between temperature T, entropy S, and total energy E: T = ∂E The existence of negative temperature is, possible in a thermodynamic system where the entropy is not restricted to a monotonically increasing function of the total energy, or, in other words where there is a state of maximum entropy [2].

Results

Conclusion