Dynamical density functional theory (DDFT) has been successfully derived and applied to describe on the one hand passive colloidal suspensions, including hydrodynamic interactions between individual particles. On the other hand, active "dry" crowds of self-propelled particles have been characterized using DDFT. Here we go one essential step further and combine these two approaches. We establish a DDFT for active microswimmer suspensions. For this purpose, simple minimal model microswimmers are introduced. These microswimmers self-propel by setting the surrounding fluid into motion. They hydrodynamically interact with each other through their actively self-induced fluid flows and via the common "passive" hydrodynamic interactions. An effective soft steric repulsion is also taken into account. We derive the DDFT starting from common statistical approaches. Our DDFT is then tested and applied by characterizing a suspension of microswimmers the motion of which is restricted to a plane within a three-dimensional bulk fluid. Moreover, the swimmers are confined by a radially symmetric trapping potential. In certain parameter ranges, we find rotational symmetry breaking in combination with the formation of a "hydrodynamic pumping state", which has previously been observed in the literature as a result of particle-based simulations. An additional instability of this pumping state is revealed.

We have performed an extensive analysis of a single-particle stochastic heat engine constructed by manipulating a Brownian particle in a time-dependent harmonic potential. The cycle consists of two isothermal steps at different temperatures and two adiabatic steps similar to that of a Carnot engine. The engine shows qualitative differences in inertial and overdamped regimes. All the thermodynamic quantities, including efficiency, exhibit strong fluctuations in a time periodic steady state. The fluctuations of stochastic efficiency dominate over the mean values even in the quasistatic regime. Interestingly, our system acts as an engine provided the temperature difference between the two reservoirs is greater than a finite critical value which in turn depends on the cycle time and other system parameters. This is supported by our analytical results carried out in the quasistatic regime. Our system works more reliably as an engine for large cycle times. By studying various model systems, we observe that the operational characteristics are model dependent. Our results clearly rule out any universal relation between efficiency at maximum power and temperature of the baths. We have also verified fluctuation relations for heat engines in time periodic steady state.

Actin and myosin assemble into a thin layer of a highly dynamic network underneath the membrane of eukaryotic cells. This network generates the forces that drive cell- and tissue-scale morphogenetic processes. The effective material properties of this active network determine large-scale deformations and other morphogenetic events. For example, the characteristic time of stress relaxation (the Maxwell time τM) in the actomyosin sets the timescale of large-scale deformation of the cortex. Similarly, the characteristic length of stress propagation (the hydrodynamic length λ) sets the length scale of slow deformations, and a large hydrodynamic length is a prerequisite for long-ranged cortical flows. Here we introduce a method to determine physical parameters of the actomyosin cortical layer in vivo directly from laser ablation experiments. For this we investigate the cortical response to laser ablation in the one-cell-stage Caenorhabditis elegans embryo and in the gastrulating zebrafish embryo. These responses can be interpreted using a coarse-grained physical description of the cortex in terms of a two-dimensional thin film of an active viscoelastic gel. To determine the Maxwell time τM, the hydrodynamic length λ, the ratio of active stress ζΔμ, and per-area friction γ, we evaluated the response to laser ablation in two different ways: by quantifying flow and density fields as a function of space and time, and by determining the time evolution of the shape of the ablated region. Importantly, both methods provide best-fit physical parameters that are in close agreement with each other and that are similar to previous estimates in the two systems. Our method provides an accurate and robust means for measuring physical parameters of the actomyosin cortical layer. It can be useful for investigations of actomyosin mechanics at the cellular-scale, but also for providing insights into the active mechanics processes that govern tissue-scale morphogenesis.

The total entropy production fluctuations are studied in some exactly solvable models. For these systems, the detailed fluctuation theorem holds even in the transient state, provided initially that the system is prepared in thermal equilibrium. The nature of entropy production during the relaxation of a system to equilibrium is analyzed. The averaged entropy production over a finite time interval gives a better bound for the average work performed on the system than that obtained from the well-known Jarzynski equality. Moreover, the average entropy production as a quantifier for information theoretic nature of irreversibility for finite time nonequilibrium processes is discussed.