Run-and-tumble motion in a linear ratchet potential: Analytic solution, power extraction, and first-passage properties

We explore the properties of run-and-tumble particles moving in a piecewise-linear "ratchet" potential by deriving analytic results for the system's steady-state probability density, current, entropy production rate, extractable power, and thermodynamic efficiency. The ratchet's broken spatial symmetry rectifies the particles' self-propelled motion, resulting in a positive current that peaks at finite values of the diffusion strength, ratchet height, and particle self-propulsion speed. Similar nonmonotonic behaviour is also observed for the extractable power and efficiency. We find the optimal apex position for generating maximum current varies with diffusion, and that entropy production can have nonmonotonic dependence on diffusion. In particular, for vanishing diffusion, entropy production remains finite when particle self-propulsion is weaker than the ratchet force. Furthermore, power extraction with near-perfect efficiency is achievable in certain parameter regimes due to the simplifications afforded by modelling "dry" active particles. In the final part, we derive mean first-passage times and splitting probabilities for different boundary and initial conditions. This work connects the study of work extraction from active matter with exactly solvable active particle models and will therefore facilitate the design of active engines through these analytic results.Comment: 14 pages (main), 23 pages (total), 17 figure

Entropy Production in Exactly Solvable Systems.

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 global 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

Active particles, ratchets and their field theories

This thesis aims to address problems in active matter by employing techniques in both stochastic processes and statistical field theories. It is mainly divided into two parts: first, applications of stochastic processes to find the entropy production of var- ious exactly solvable models and solve the dynamics of a Run-and-Tumble particle in a piecewise linear potential, and second, applications of field theories to find the optimal shape for maximising currents of a Run-and-Tumble particle perturbatively and probing the particle identities using different field theories. In Chapter 1, I de- rive various methods and results from stochastic processes that are used in the rest of the thesis. In Chapter 2, I present a self-contained review of entropy production and calculate it from first principles for various exactly solvable models. In Chap- ter 3, I solve the steady-state dynamics of a Run-and-Tumble particle in a piece- wise linear ratchet and calculate various other quantities such as particle current, entropy production and mean first passage time. In Chapter 4, I derive and present Doi-Peliti field theory and response field theory which are used in the rest of the the- sis. In Chapter 5, I present a method of solving the probability distribution perturba- tively and finding the optimal shape of the potential that maximises the probability current for a Run-and-Tumble particle using Doi-Peliti field theory. In Chapter 6, I identify the mechanism where particle entity is enforced in the context of the Doi- Peliti field theory of a diffusive particle and the response field theory that is derived from Dean’s equation.Open Acces

Particle Entity in the Doi-Peliti and Response Field Formalisms

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

Advanced Biofuels and Beyond: Chemistry Solutions for Propulsion and Production

Leitner W, Klankermayer J, Pischinger S, Pitsch H, Kohse-Höinghaus K. Advanced Biofuels and Beyond: Chemistry Solutions for Propulsion and Production. Angewandte Chemie International Edition. 2017;56(20):5412-5452

Synthese, motorische Verbrennung, Emissionen: Chemische Aspekte des Kraftstoffdesigns

Leitner W, Klankermayer J, Pischinger S, Pitsch H, Kohse-Höinghaus K. Synthese, motorische Verbrennung, Emissionen: Chemische Aspekte des Kraftstoffdesigns. Angewandte Chemie. 2017;129(20):5500-5544