  Many measurements on soft condensed matter (e.g., biological and materials)
systems track low-dimensional observables projected from the full system phase
space as a function of time. Examples are dynamic structure factors,
spectroscopic and rheological response functions, and time series of distances
derived from optical tweezers, single-molecule spectroscopy and molecular
dynamics simulations. In many such systems the projection renders the reduced
dynamics non-Markovian and the observable is not prepared in, or initially
sampled from and averaged over, a stationary distribution. We prove that such
systems always exhibit non-equilibrium, time asymmetric dynamics. That is, they
evolve in time with a broken time-translation invariance in a manner closely
resembling aging dynamics. We identify the entropy associated with the breaking
of time-translation symmetry that is a measure of the instantaneous
thermodynamic displacement of latent, hidden degrees of freedom from their
stationary state. Dynamical time asymmetry is a general phenomenon, independent
of the underlying energy surface, and is frequently even visible in
measurements on systems that have fully reached equilibrium. This finding has
fundamental implications for the interpretation of many experiments on, and
simulations of, biological and materials systems.
