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The study of motility control by smart agents offers a promising platform for systematically exploring the fundamental physical constraints underlying the functioning of bio-inspired micro-machines operating far from equilibrium. Here, we address the question of the energy cost required for a self-steering active agent to localise itself within a specific region of space or follow a pre-defined trajectory under the influence of fluctuations and external flows. Building on a stochastic thermodynamic formulation of the problem, we derive a generic relationship between dissipation and localisation accuracy, which reveals a fundamental dissipation-accuracy tradeoff constraining the agent's performance. In addition, we illustrate how our framework enables the derivation of optimal steering policies that achieve localisation at minimum energy expenditure., Comment: 32 pages (18 in main text), 8 figures

The Ornstein-Uhlenbeck (OU) process describes the dynamics of Brownian particles in a confining harmonic potential, thereby constituting the paradigmatic model of overdamped, mean-reverting Langevin dynamics. Despite its widespread applicability, this model falls short when describing physical systems where the confining potential is itself subjected to stochastic fluctuations. However, such stochastic fluctuations generically emerge in numerous situations, including in the context of colloidal manipulation by optical tweezers, leading to inherently out-of-equilibrium trapped dynamics. To explore the consequences of stochasticity at this level, we introduce a natural extension of the OU process, in which the stiffness of the harmonic potential is itself subjected to OU-like fluctuations. We call this model the OU$^2$ process. We examine its statistical, dynamic, and thermodynamic properties through a combination of analytical and numerical methods. Importantly, we show that the probability density for the particle position presents power-law tails, in contrast to the Gaussian decay of the standard OU process. In turn, this causes the trapping behavior, extreme value statistics, first passage statistics, and entropy production of the OU$^2$ process to differ qualitatively from their standard OU counterpart. Due to the wide applicability of the standard OU process and of the proposed OU$^2$ generalisation, our study sheds light on the peculiar properties of stochastic dynamics in random potentials and lays the foundation for the refined analysis of the dynamics and thermodynamics of numerous experimental systems., Comment: 32 pages, 7 figures

Nonreciprocal interactions are commonplace in continuum-level descriptions of both biological and synthetic active matter, yet studies addressing their implications for time-reversibility have so far been limited to microscopic models. Here, we derive a general expression for the average rate of informational entropy production in the most generic mixture of conserved phase fields with nonreciprocal couplings and additive conservative noise. For the particular case of a binary system with Cahn-Hilliard dynamics augmented by nonreciprocal cross-diffusion terms, we observe a non-trivial scaling of the entropy production rate across a parity-time symmetry breaking phase transition. We derive a closed-form analytic expression in the weak-noise regime for the entropy production rate due to the emergence of a macroscopic dynamic phase, showing it can be written in terms of the global polar order parameter, a measure of parity-time symmetry breaking., Comment: 8 pages (3 figures) of main text + 10 pages (2 figures) of supplementary information

Static nonreciprocal forces between particles generically drive persistent motion reminiscent of self-propulsion. Here, we demonstrate that reciprocity-breaking fluctuations about a reciprocal mean coupling strength are sufficient to generate this behavior in a minimal two-particle model, with the velocity of the ensuing \textit{active} bound state being modulated in time according to the nature of these fluctuations. To characterize the ensuing nonequilibrium dynamics, we derive exact results for the time-dependent center of mass mean-squared displacement and average rate of entropy production for two simple examples of discrete- and continuous-state fluctuations. We find that the resulting dimer can exhibit unbiased persistent motion akin to that of an active particle, leading to a significantly enhanced effective diffusivity., Comment: 6 pages (3 figures) of main text + 10 pages (3 figures) of supplementary information

We identify generic protocols achieving optimal power extraction from a single active particle subject to continuous feedback control under the assumption that its spatial trajectory, but not its instantaneous self-propulsion force, is accessible to direct observation. Our Bayesian approach draws on the Onsager-Machlup path integral formalism and is exemplified in the cases of free run-and-tumble and active Ornstein-Uhlenbeck dynamics in one dimension. Such optimal protocols extract positive work even in models characterised by time-symmetric positional trajectories and thus vanishing informational entropy production rates. We argue that the theoretical bounds derived in this work are those against which the performance of realistic active matter engines should be compared., Comment: 19 pages (including supplementary)

We introduce a procedure to test a theory for point particle entity, that is, whether said theory takes into account the discrete nature of the constituents of the system. We then identify the mechanism whereby particle entity is enforced in the context of two field-theoretic frameworks designed to incorporate the particle nature of the degrees of freedom, namely the Doi-Peliti field theory and the response field theory that derives from Dean's equation. While the Doi-Peliti field theory encodes the particle nature at a very fundamental level that is easily revealed, demonstrating the same for Dean's equation is more involved and results in a number of surprising diagrammatic identities. We derive those and discuss their implications. These results are particularly pertinent in the context of active matter, whose surprising and often counterintuitive phenomenology rests wholly on the particle nature of the agents and their degrees of freedom as particles.

A positive rate of entropy production at steady state is a distinctive feature of truly non-equilibrium processes. Exact results, while being often limited to simple models, offer a unique opportunity to explore the thermodynamic features of these processes in full details. Here we derive analytical results for the steady-state rate of entropy production in single particle systems driven away from equilibrium by the fluctuations of an external potential of arbitrary shapes. Subsequently, we provide exact results for a diffusive particle in a harmonic trap whose potential stiffness varies in time according to both discrete and continuous Markov processes. In particular, studying the case of a fully intermittent potential allows us to introduce an effective model of stochastic resetting for which it is possible to obtain finite non-negative entropy production. Altogether, this work lays the foundation for a non-equilibrium thermodynamic theory of fluctuating potentials, with immediate applications to stochastic resetting processes, fluctuations in optical traps and fluctuating interactions in living systems., Comment: 27 pages, 9 figures

Entropy production plays a fundamental role in the study of non-equilibrium systems by offering a quantitative handle on the degree of time-reversal symmetry breaking. It depends crucially on the degree of freedom considered as well as on the scale of description. It was hitherto unknown how the entropy production at one resolution of the degrees of freedom is related to the entropy production at another resolution. This relationship is of particular relevance to coarse grained and continuum descriptions of a given phenomenon. In this work, we derive the scaling of the entropy production under iterative coarse graining on the basis of the correlations of the underlying microscopic transition rates. Our approach unveils a natural criterion to distinguish equilibrium-like and genuinely non-equilibrium macroscopic phenomena based on the sign of the scaling exponent of the entropy production per mesostate., Comment: 21 pages, 6 figures

The rate of entropy production by a stochastic process quantifies how far it is from thermodynamic equilibrium. Equivalently, entropy production captures the degree to which detailed balance and time-reversal symmetry are broken. Despite abundant references to entropy production in the literature and its many applications in the study of non-equilibrium stochastic particle systems, a comprehensive list of typical examples illustrating the fundamentals of entropy production is lacking. Here, we present a brief, self-contained review of entropy production and calculate it from first principles in a catalogue of exactly solvable setups, encompassing both discrete- and continuous-state Markov processes, as well as single- and multiple-particle systems. The examples covered in this work provide a stepping stone for further studies on entropy production of more complex systems, such as many-particle active matter, as well as a benchmark for the development of alternative mathematical formalisms., Comment: 33 pages, 13 figures

Among observables characterising the random exploration of a graph or lattice, the cover time, namely the time to visit every site, continues to attract widespread interest. Much insight about cover times is gained by mapping to the (spaceless) coupon-collector problem, which amounts to ignoring spatio-temporal correlations, and an early conjecture that the limiting cover time distribution of regular random walks on large lattices converges to the Gumbel distribution in $d \geq 3$ was recently proved rigorously. Furthermore, a number of mathematical and numerical studies point to the robustness of the Gumbel universality to modifications of the \textit{spatial} features of the random search processes (e.g.\ introducing persistence and/or intermittence, or changing the graph topology). Here we investigate the robustness of the Gumbel universality to dynamical modification of the \textit{temporal} features of the search, specifically by allowing the random walker to "accelerate" or "decelerate" upon visiting a previously unexplored site. We generalise the mapping mentioned above by relating the statistics of cover times to the roughness of $1/f^\alpha$ Gaussian signals, leading to the conjecture that the Gumbel distribution is but one of a family of cover time distributions, ranging from Gaussian for highly accelerated cover, to exponential for highly decelerated cover. While our conjecture is confirmed by systematic Monte Carlo simulations in dimensions $d > 3$, our results for acceleration in $d=3$ challenge the current understanding of the role of correlations in the cover time problem., Comment: 10 pages, 15 figures

We study the physics of turbulent/non-turbulent interface of an isolated turbulent region in dilute polymer solutions and Newtonian fluid. The performance of a FENE-P model with a localized homogeneous forcing is verified using the specially designed experimental setup of a turbulent patch growing in water/dilute polymer solution, without mean shear and far from the walls. The results of the small scale dynamics of vorticity and strain help to reveal the key mechanism of polymer action in turbulent flows without mean shear. Modified degrees of alignment between vorticity, the polymer conformation and the rate-of-strain tensors found especially near the interface explain the reduced vorticity stretching and increased vorticity compression terms. These small scale alignments in the non-Newtonian turbulent flow thus lead to a reduced production of enstrophy and consequently to a reduced entrainment (seen as propagation or dispersion).

In this work we present the architecture and results of a fully digital Front End Electronics (FEE) read out system developed for the GALILEO array. The FEE system, developed in collaboration with the Advanced Gamma Tracking Array (AGATA) collaboration, is composed of three main blocks: preamplifiers, digitizers and preprocessing electronics. The slow control system contains a custom Linux driver, a dynamic library and a server implementing network services. The digital processing of the data from the GALILEO germanium detectors has demonstrated the capability to achieve an energy resolution of 1.53 per mil at an energy of 1.33 MeV., Comment: 5 pages, 6 figures, preprint version of IEEE Transactions on Nuclear Science paper submitted for the 19th IEEE Real Time Conference

The Advanced GAmma Tracking Array (AGATA) is a European project to develop and operate the next generation gamma-ray spectrometer. AGATA is based on the technique of gamma-ray energy tracking in electrically segmented high-purity germanium crystals. This technique requires the accurate determination of the energy, time and position of every interaction as a gamma ray deposits its energy within the detector volume. Reconstruction of the full interaction path results in a detector with very high efficiency and excellent spectral response. The realization of gamma-ray tracking and AGATA is a result of many technical advances. These include the development of encapsulated highly-segmented germanium detectors assembled in a triple cluster detector cryostat, an electronics system with fast digital sampling and a data acquisition system to process the data at a high rate. The full characterization of the crystals was measured and compared with detector-response simulations. This enabled pulse-shape analysis algorithms, to extract energy, time and position, to be employed. In addition, tracking algorithms for event reconstruction were developed. The first phase of AGATA is now complete and operational in its first physics campaign. In the future AGATA will be moved between laboratories in Europe and operated in a series of campaigns to take advantage of the different beams and facilities available to maximize its science output. The paper reviews all the achievements made in the AGATA project including all the necessary infrastructure to operate and support the spectrometer., Comment: This version contains a correction of a typing error in the caption of Fig. 2. The DOI to the article published in Nucl. Instr. Meth A was also added