Figure 1: A schematic illustration of the relationship between density, density fluctuations, and temperature in a one-dimensional Fermi gas. The three grids represent a 1D phase space, with axes $x$ and $p_x$. Each box represents a phase-space cell (with volume = $h$). At most, one particle is permitted per box. The density corresponds to the number of atoms per column. The temperature is related to how the number of atoms per row decreases with $p_x$. A higher temperature means more population in high momentum states. (a) A cold dense gas. (b) A cold but less dense gas. (c) A dense but hotter gas. The density fluctuations (that is, the variance in the number of particles per column) are lowest in (a). If the absolute density is known, a measurement of the density fluctuations gives information about the absolute temperature. This relationship is embodied in the fluctuation and dissipation theorem.