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The relationship between 2D $SO(2,1)$ conformal anomalies in nonrelativisticsystems and the virial expansion is explored using recently developedpath-integral methods. In the process, the Beth-Uhlenbeck formula for the shiftof the second virial coefficient $\delta b_2$ is obtained, as well as a virialexpansion for the Tan contact. A possible extension of these techniques forhigher orders in the virial expansion is discussed.

Virial expansion for the Tan contact and Beth-Uhlenbeck formula from 2D SO(2,1) anomalies