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 px. 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 px. 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.