<div>In the 1970's, Arthur Ashkin developed a remarkable system called the ``optical tweezer'' which utilizes the radiation pressure of light to manipulate particles. Because of its non-invasive nature and controllability, optical tweezers have been widely adopted in biology, chemistry and physics. In this dissertation, two applications related to optical tweezers will be discussed. The first application is about the demonstration of multiple feedback controlled optical tweezers which let us conduct novel experiments which have not been performed before. For the second application, levitation of a silica nanodumbbell and cooling its motion in five degrees of freedom is executed.</div><div><br></div><div>To be more specific, the first chapter of the thesis focuses on an experiment using the feedback controlled optical tweezers in water. A well-known thought experiment called ``Feynman's ratchet and pawl'' is experimentally demonstrated. Feynman’s ratchet is a microscopic heat engine which can rectify the random thermal fluctuation of molecules to harness useful work. After Feynman proposed this system in the 1960’s, it has drawn a lot of interest. In this dissertation, we demonstrate a solvable model of Feynman’s ratchet using a silica nanoparticle inside a feedback controlled one dimensional optical trap. The idea and techniques to realize two separate thermal reservoirs and to keep them in contact with the ratchet is discussed in detail. Also, both experiment and simulation about the characteristics of our system as a heat engine are fully explored.</div><div><br></div><div>In the latter part of the dissertation, trapping silica nanodumbbell in vacuum and cooling its motion in five degrees of freedom is discussed. A levitated nanoparticle in vacuum is an extraordinary optomechanical system with an exceptionally high mechanical quality factor. Therefore, levitated particles are often utilized as a sensor in various research. Different from a levitated single nanosphere, which is only sensitive to force, a levitated nanodumbbell is sensitive to both force and torque. This is due to the asymmetry of the particle resulting it to have three rotational degrees of freedoms as well as three translational degrees of freedoms. In this dissertation, creating and levitating a silica nanodumbbell will be demonstrated. Active feedback cooling also known as cold damping will be employed to stabilize and cool the two torsional degrees of freedom of the particle along with the three center of mass DOF in vacuum. Additionally, both computational and experimental analysis is conducted on a levitated nanodumbbell which we call rotation-coupled torsional motion. The complex torsional motion can be fully explained with the effects of both thermal nonlinearity and rotational coupling. The new findings and knowledge of a levitated non-spherical particles leads us one step further towards levitated optomechanics with more complex particles.</div>

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This thesis is devoted to the theoretical study of slow thermodynamic processes in non-equilibrium stochastic systems. Its main result is a physically and mathematically consistent construction of relevant thermodynamic quantities in the quasistatic limit for a large class of non-equilibrium models. As an application of general methods a natural non-equilibrium generalization of heat capacity is introduced and its properties are analyzed in detail, including an anomalous far-from-equilibrium behavior. The developed methods are further applied to the related problem of time-scale separation where they enable to describe the effective dynamics of both slow and fast degrees of freedom in a more precise way. Powered by TCPDF (www.tcpdf.org)

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Avec les progrès de la technologie, il est désormais devenu possible de manipuler des faibles quantités d’objets nanométriques, voire des objets uniques. Observer une réaction chimique de quelques centaines de molécules sur des catalyseurs, étudier le travail exercé lors du déploiement d’un brin d’ADN unique ou mesurer la chaleur émise par un unique électron dans un circuit électrique constituent aujourd’hui des actes expérimentaux courants. Cependant, à cette échelle, le caractère aléatoire des processus physiques étudiés se fait plus fortement ressentir. Développer une théorie thermodynamique à ces échelles nécessite d'y inclure de manière exhaustive ces fluctuations.Ces préoccupations et les résultats expérimentaux et théoriques associés ont mené à l’émergence de ce que l’on appelle aujourd’hui la thermodynamique stochastique. Cette thèse se propose de développer une approche originale à la thermodynamique stochastique, basée sur une extension de l'hypothèse d'équilibre local aux variables fluctuantes d'un système. Cette théorie offre de nouvelles définitions des grandeurs thermodynamiques stochastiques, dont l'évolution est donnée par des équations différentielles stochastiques (EDS).Nous avons choisi d'étudier cette théorie à travers des modèles simplifiés de phénomènes physiques variés; transport (diffusif) de chaleur ou de masse, transport couplé (comme la thermodiffusion), ainsi que des modèles de réactions chimiques linéaires et non-linéaires. A travers ces exemples, nous avons proposé des versions stochastiques de plusieurs grandeurs thermodynamiques d'intérêt. Une large part de cette thèse est dévolue à l'entropie et aux différents termes apparaissant dans son bilan (flux d'entropie, production d'entropie ou dissipation). D'autres exemples incluent l'énergie libre d'Helmholtz, la production d'entropie d'excès, ou encore les efficacités thermodynamiques dans le transport couplé.A l'aide de cette théorie, nous avons étudié les propriétés statistiques de ces différentes grandeurs, et plus particulièrement l'effet des contraintes thermodynamiques ainsi que les propriétés cinétiques du modèle sur celles-là. Dans un premier temps, nous montrons comment l'état thermodynamique d'un système (à l' équilibre ou hors d'équilibre) contraint la forme de la distribution de la production d'entropie. Au-delà de la production d'entropie, cette contrainte apparaît également pour d'autres quantités, comme l'énergie libre d'Helmholtz ou la production d'entropie d'excès. Nous montrons ensuite comment des paramètres de contrôle extérieurs peuvent induire des bimodalités dans les distributions d'efficacités stochastiques.Les non-linéarités de la cinétique peuvent également se répercuter sur la thermodynamique stochastique. En utilisant un modèle non-linéaire de réaction chimique, le modèle de Schlögl, nous avons calculé la dissipation moyenne, non-nulle, engendrée par les fluctuations du système. Les non-linéarités offrent aussi la possibilité de produire des bifurcations dans le système. Les différentes propriétés statistiques (moments et distributions) de la production d'entropie ont été étudiées à différents points avant, pendant et après la bifurcation dans le modèle de Schlögl.Ces nombreuses propriétés ont été étudiées via des développements analytiques supportés par des simulations numériques des EDS du système. Nous avons ainsi pu montrer la fine connexion existant entre les équations cinétiques du système, les contraintes thermodynamiques et les propriétés statistiques des fluctuations de différentes grandeurs thermodynamiques stochastiques. / Over the last decades, nanotechnology has experienced great steps forwards, opening new ways to manipulate micro- and nanosystems. These advances motivated the development of a thermodynamic theory for such systems, taking fully into account the unavoidable fluctuations appearing at that scale. This ultimately leads to an ensemble of experimental and theoretical results forming the emergent field of stochastic thermodynamics. In this thesis, we propose an original theoretical approach to stochastic thermodynamics, based on the extension of the local equilibrium hypothesis (LEH) to fluctuating variables in small systems. The approach provides new definitions of stochastic thermodynamic quantities, whose evolution is given by stochastic differential equations (SDEs).We applied this new formalism to a diverse range of systems: heat or mass diffusive transport, coupled transport phenomena (thermodiffusion), and linear or non-linear chemical systems. In each model, we used our theory to define key stochastic thermodynamic quantities. A great emphasis has been put on entropy and the different contributions to its evolution (entropy flux and entropy production) throughout this thesis. Other examples include also the stochastic Helmholtz energy, stochastic excess entropy production and stochastic efficiencies in coupled transport. We investigated how the statistical properties of these quantities are affected by external thermodynamic constraints and by the kinetics of the system. We first studied how the thermodynamic state of the system (equilibrium \textit{vs.} non-equilibrium) strongly impacts the distribution of entropy production. We then extended those findings to other related quantities, such as the Helmholtz free energy and excess entropy production. We also analysed how some external control parameters could lead to bimodality in stochastic efficiencies distributions.In addition, non-linearities affect stochastic thermodynamics quantities in different ways. Using the example of the Schlögl chemical model, we computed the average dissipation of the fluctuations in a non-linear system. Such systems can also undergo a bifurcation, and we studied how the moments and the distribution of entropy production change while crossing the critical point.All these properties were investigated with theoretical analyses and supported by numerical simulations of the SDEs describing the system. It allows us to show that properties of the evolution equations and external constraints could strongly reflect in the statistical properties of stochastic thermodynamic quantities. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

We characterize finite-time thermodynamic processes of multidimensional quadratic overdamped systems. Analytic expressions are provided for heat, work, and dissipation for any evolution of the system covariance matrix. The Bures-Wasserstein metric between covariance matrices naturally emerges as the local quantifier of dissipation. General principles of how to apply these geometric tools to identify optimal protocols are discussed. Focusing on the relevant slow-driving limit, we show how these results can be used to analyze cases in which the experimental control over the system is partial.

Les petites machines, comme les moteurs moléculaires ou les particules actives, fonctionnent dans un environnement fortement fluctuant qui affecte leur efficacité ou leur puissance. L'objectif de cette thèse est de décrire les petites machines à l'aide de la thermodynamique stochastique et de la théorie des grandes déviations. En reliant localement puis globalement les courants aux forces thermodynamiques, on introduit une matrice de conductance hors d'équilibre, qui généralise la matrice d'Onsager pour un système stationnaire hors d'équilibre. Cela permet de majorer l'efficacité des machines par une fonction universelle qui ne dépend que du degré de couplage entre les courants d'entrée et de sortie. On obtient aussi de nouvelles relations générales entre puissance et efficacité. Du point de vue des fluctuations, la matrice de conductance hors d'équilibre est reliée à une borne quadratique pour les fonctions de grande déviation des courants. Cette borne permet d'obtenir des bornes pour les fonctions de grande déviation de l'efficacité, mais aussi de revisiter le théorème de fluctuation-dissipation comme une inégalité dans le cas des systèmes loin de l'équilibre. Pour terminer, on étudie l'effet d'une brisure d'ergodicité sur les fluctuations d'observables comme l'activité, les courants ou l'efficacité. En particulier, on calcule la fonction de grande déviation de l'efficacité pour un ensemble de nanomachines en interaction pour lesquelles un couplage fort et une brisure d'ergodicité apparaissent à la limite thermodynamique. / Small machines -- like molecular motors or active particles -- operate in highly fluctuating environments that affect their efficiency and power. This thesis aims at describing small machines using stochastic thermodynamics and large deviation theory. By relating mean currents to thermodynamic forces, locally first and then at the global level, we introduce the non-equilibrium conductance matrix that generalizes the Onsager matrix for stationary non-equilibrium systems. We use it to bound machine efficiency by a universal function depending only on the degree of coupling between input and output currents and to find new general power-efficiency trade-offs. On the fluctuations side, the non-equilibrium conductance matrix can be used to find a quadratic bound on the large deviation function of currents. This enables to revisit the fluctuation-dissipation theorem as an inequality when dealing with far-from-equilibrium systems, but also to derive bounds on the efficiency large deviation function. Finally, we study the effects of ergodicity breaking on the fluctuations of observables like activity, currents or efficiency. In particular, we derive the efficiency large deviation function for a model of interacting nanomachines, for which tight coupling and ergodicity breaking emerge in the thermodynamic limit.

Stochastic processes with temporal delay play an important role in science and engineering whenever finite speeds of signal transmission and processing occur. However, an exact mathematical analysis of their dynamics and thermodynamics is available for linear models only. We introduce a class of stochastic delay processes with nonlinear time-local forces and linear time-delayed forces that obey fluctuation theorems and converge to a Boltzmann equilibrium at long times. From the point of view of control theory, such ‘equilibrium stochastic delay processes’ are stable and energetically passive, by construction. Computationally, they provide diverse exact constraints on general nonlinear stochastic delay problems and can, in various situations, serve as a starting point for their perturbative analysis. Physically, they admit an interpretation in terms of an underdamped Brownian particle that is either subjected to a time-local force in a non-Markovian thermal bath or to a delayed feedback force in a Markovian thermal bath. We illustrate these properties numerically for a setup familiar from feedback cooling and point out experimental implications.

Title: Stochastic dynamics and energetics of biomolecular systems Author: Artem Ryabov Department: Department of Macromolecular Physics Supervisor: prof. RNDr. Petr Chvosta, CSc., Department of Macromolecular Physics Abstract: The thesis comprises exactly solvable models from non-equilibrium statistical physics. First, we focus on a single-file diffusion, the diffusion of particles in narrow channel where particles cannot pass each other. After a brief review, we discuss open single-file systems with absorbing boundaries. Emphasis is put on an interplay of absorption process at the boundaries and inter-particle entropic repulsion and how these two aspects affect the dynam- ics of a given tagged particle. A starting point of the discussions is the exact distribution for the particle displacement derived by order-statistics argu- ments. The second part of the thesis is devoted to stochastic thermodynam- ics. In particular, we present an exactly solvable model, which describes a Brownian particle diffusing in a time-dependent anharmonic potential. The potential has a harmonic component with a time-dependent force constant and a time-independent repulsive logarithmic barrier at the origin. For a particular choice of the driving protocol, the exact work characteristic func- tion is obtained. An asymptotic analysis of...

Cellular decision-making help cells to infer functionally different phenotypes in response to microenvironmental cues and noise present in the system and the environment, with or without genetic change. In Cellular Biology, there exists a list of open questions such as, how individual cell decisions influence the dynamics at the population level (an organization of indistinguishable cells) and at the tissue level (a group of nearly identical cells and their corresponding extracellular matrix which simultaneously accomplish a set of biological operations)? As collective cell migration originates from local cellular orientation decisions, can one generate a mathematical model for collective cell migration phenomena without elusive undiscovered biophysical/biochemical mechanisms and further predict the pattern formations which originates inside the collective cell migration? how optimal microenvironmental sensing is related to differentiated tissue at the spatial scale ? How cell sensing radius and total entropy production (which precisely helps us to understand the operating regimes where cells can take decisions about their future fate) is correlated, and how can one understand the limits of sensing radius at robust tissue development ? To partially tackle these sets of questions, the LEUP (Least microEnvironmental Uncertainty Principle) hypothesis has been applied to different biological scenaros. At first, the LEUP has been enforced to understand the spatio-temporal behavior of a tissue exhibiting phenotypic plasticity (it is a prototype of cell decision-making). Here, two cases have been rigorously studied i.e., migration/resting and migration/proliferation plasticity which underlie the epithelial-mesenchymal transition (EMT) and the Go-or-Grow dichotomy. On the one hand, for the Go-or-Rest plasticity, a bistable switching mechanism between a diffusive (fluid) and an epithelial (solid) tissue phase has been observed from an analogous mean-field approximation which further depends on the sensitivity of the phenotypes to the microenvironment. However, on the other hand, for the Go-or-Grow plasticity, the possibility of Turing pattern formation is inspected for the “solid” tissue phase and its relation to the parameters of the LEUP-driven cell decisions. Later, LEUP hypothesis has been suggested in the area of collective cell migration such that it can provide a tool for a generative mathematical model of collective migration without precise knowledge about the mechanistic details, where the famous Vicsek model is a special case. In this generative model of collective cell migration, the origin of pattern formation inside collective cell migration has been investigated. Moreover, this hypothesis helps to construct a mathematical model for the collective behavior of spherical \textit{Serratia marcescens} bacteria, where the basic understanding of migration mechanisms remain unknown. Furthermore, LEUP has been applied to understand tissue robustness, which in turn shows the way how progenitor cell fate decisions are associated with environmental sensing. The regulation of environmental sensing drives the robustness of the spatial and temporal order in which cells are generated towards a fully differentiating tissue, which are verified later with the experimental data. LEUP driven stochastic thermodynamic formalism also shows that the thermodynamic robustness of differentiated tissues depends on cell metabolism, cell sensing properties and the limits of the cell sensing radius, which further ensures the robustness of differentiated tissue spatial order. Finally, all important results of the thesis have been encapsulated and the extension of the LEUP has been discussed.:Contents Statement of authorship vii Abstract ix I. Introduction to cell decision-making 1 1. What is cell decision-making ? 3 1.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2. Examplesofcelldecision-making. . . . . . . . . . . . . . . . . . . . . . 4 1.2.1. PhenotypicPlasticity . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2.2. Cellularmigration:orientationdecisions . . . . . . . . . . . . . 5 1.2.3. Celldifferentiation . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.3. Challengesandopenquestions . . . . . . . . . . . . . . . . . . . . . . 7 1.4. Solutionstrategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.5. Structureofthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 II. Least microEnvironmental Uncertainty Principle (LEUP) 11 2. Least microEnvironmental Uncertainty Principle (LEUP) 13 2.1. HypothesisbehindLEUP . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.2. Mathematicalformulation . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.2.1. CellasBayesiandecisionmaker . . . . . . . . . . . . . . . . . . 14 2.2.2. VariationalprincipleforLEUP . . . . . . . . . . . . . . . . . . . . 16 III. LEUP in biological problems 17 3. Phenotypic plasticity : dynamics at the level of tissue from individual cell decisions 19 3.1. Mathematicalframework . . . . . . . . . . . . . . . . . . . . . . . . . . 20 3.2. Individualbasedmodel(IBM) . . . . . . . . . . . . . . . . . . . . . . . . 22 3.3. Mean-fieldapproximation . . . . . . . . . . . . . . . . . . . . . . . . . . 24 3.3.1. Phenotypicswitchingdynamics . . . . . . . . . . . . . . . . . . 26 3.3.2. Cellmigrationdynamics . . . . . . . . . . . . . . . . . . . . . . . 28 3.3.3. Superpositionofphenotypicswitchingdynamicsandcellmi- gration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 3.4. Spatio-temporaldynamicsofcellmigration/proliferationplasticity . . 28 3.4.1. CaseI:Largeinteractionradius . . . . . . . . . . . . . . . . . . 29 3.4.2. CaseII:Finiteinteractionradius . . . . . . . . . . . . . . . . . . 30 3.4.3. Phenotypicswitchingdynamicsintheabsenceofmicroenvi- ronmentalsensing . . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.5. Summaryandoutlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 4. Cellular orientation decisions: origin of pattern formations in collective cell migrations 39 4.1. Mathematicalframework . . . . . . . . . . . . . . . . . . . . . . . . . . 40 4.1.1. Self-propelledparticlemodelwithleupbaseddecision-making 41 4.1.2. Orderparametersandobservables . . . . . . . . . . . . . . . . 42 4.1.3. Statisticaltest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 4.2. ComparisonwithVicsekmodel . . . . . . . . . . . . . . . . . . . . . . . 43 4.2.1. Patternsindifferentparameterregimes . . . . . . . . . . . . . 45 4.3. Application:thesphericalbacteriacase. . . . . . . . . . . . . . . . . . 47 4.4. Summaryandoutlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 5. Cell differentiation and sensing: tissue robustness from optimal environ- mental sensing 53 5.1. LEUPbasedmathematicalmodelforcelldifferentiation . . . . . . . . 56 5.1.1. StatisticalresultsfromLEUP . . . . . . . . . . . . . . . . . . . . 59 5.2. RelationbetweenLEUPandcellsensing . . . . . . . . . . . . . . . . . 60 5.3. LEUPdrivenfluctuationtheorem: confirmsthethermodynamicro- bustnessofdifferentiatedtissues . . . . . . . . . . . . . . . . . . . . . 61 5.3.1. Application: differentiated photoreceptor mosaics are ther- modynamicallyrobust . . . . . . . . . . . . . . . . . . . . . . . . 65 5.4. Thelimitforcellsensingradius . . . . . . . . . . . . . . . . . . . . . . . 67 5.4.1. Application:Theaveragesensingradiusoftheavianconecell 69 5.5. Summaryandoutlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 6. Discussions 75 7. Supplementary Material 91 8. Erklärung 115