Intertemporal implications of the mixture-of-distributions hypothesis (MDH) are derived based on the concept of time reversibility in statistical mechanics. The restrictions are tested using simple nonparametric tests that do not impose auxiliary assumptions on the stochastic process for trading volume, price volatility or information arrivals. The tests reject the standard MDH with one latent factor. In particular, shocks to volatility and volume are temporally asymmetric, contrary to the predictions of the MDH. The results indicate that multifactor models are needed to explain the dynamics of the volume-volatility relation.