Dissipation and asymmetry in non-equilibrium processes

For a system described by a multivariate probability density function obeying the fluctuation theorem, the average dissipation is lower-bounded by the degree of asymmetry of the marginal distributions (namely the relative entropy between the marginal and its mirror image). We formally prove that such lower bound is tighter than the recently reported bound expressed in terms of the precision of the marginal (i.e., the thermodynamic uncertainty relation) and is saturable. We illustrate the result with examples and generalisations, and employ it to experimentally improve estimates of the minimal dissipation occurring during the operation of a quantum annealer.