We compute probability distributions of trajectory observables for reversible and irreversible growth processes. These results reveal a correspondence between reversible and irreversible processes, at particular points in parameter space, in terms of their typical and atypical trajectories. Thus key features of growth processes can be insensitive to the precise form of the rate constants used to generate them, recalling the insensitivity to microscopic details of certain equilibrium behavior. We obtained these results using a sampling method, inspired by the "s-ensemble" large-deviation formalism, that amounts to umbrella sampling in trajectory space. The method is a simple variant of existing approaches, and applies to ensembles of trajectories controlled by the total number of events. It can be used to determine large-deviation rate functions for trajectory observables in or out of equilibrium.

Active biological systems reside far from equilibrium, dissipating heat even in their steady state, thus requiring an extension of conventional equilibrium thermodynamics and statistical mechanics. In this Letter, we have extended the emerging framework of stochastic thermodynamics to active matter. In particular, for the active Ornstein-Uhlenbeck model, we have provided consistent definitions of thermodynamic quantities such as work, energy, heat, entropy, and entropy production at the level of single, stochastic trajectories and derived related fluctuation relations. We have developed a generalization of the Clausius inequality, which is valid even in the presence of the non-Hamiltonian dynamics underlying active matter systems. We have illustrated our results with explicit numerical studies.

Summary C. elegans 21U-RNAs are equivalent to the piRNAs discovered in other metazoans and have important roles in gametogenesis and transposon control. The biogenesis and molecular function of 21U-RNAs and piRNAs are poorly understood. Here, we demonstrate that transcription of each 21U-RNA is regulated separately through a conserved upstream DNA motif. We use genomic analysis to show that this motif is associated with low nucleosome occupancy, a characteristic of many promoters that drive expression of protein-coding genes, and that RNA polymerase II is localized to this nucleosome-depleted region. We establish that the most conserved 8-mer sequence in the upstream region of 21U-RNAs, CTGTTTCA, is absolutely required for their individual expression. Furthermore, we demonstrate that the 8-mer is specifically recognized by Forkhead family (FKH) transcription factors and that 21U-RNA expression is diminished in several FKH mutants. Our results suggest that thousands of small non-coding transcription units are regulated by FKH proteins.

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Off-lattice active Brownian particles form clusters and undergo phase separation even in the absence of attractions or velocity-alignment mechanisms. Arguments that explain this phenomenon appeal only to the ability of particles to move persistently in a direction that fluctuates, but existing lattice models of hard particles that account for this behavior do not exhibit phase separation. Here we present a lattice model of active matter that exhibits motility-induced phase separation in the absence of velocity alignment. Using direct and rare-event sampling of dynamical trajectories, we show that clustering and phase separation are accompanied by pronounced fluctuations of static and dynamic order parameters. This model provides a complement to off-lattice models for the study of motility-induced phase separation.