Sarah A.M. Loos

University of Cambridge | Cam · Department of Applied Mathematics and Theoretical Physics

To establish general principles of optimal control of active matter, we study the elementary problem of moving an active particle by a trap with minimum work input. We show analytically that (open-loop) optimal protocols are not affected by activity, but work fluctuations are always increased. For closed-loop protocols, which rely on initial measur...

Optimizing the energy efficiency of driving processes provides valuable insights into the underlying physics and is of crucial importance for numerous applications, from biological processes to the design of machines and robots. Knowledge of optimal driving protocols is particularly valuable at the microscale, where energy supply is often limited....

We develop a framework for the stochastic thermodynamics of a probe coupled to a fluctuating medium with spatio-temporal correlations, described by a scalar field. For a Brownian particle dragged by a harmonic trap through a fluctuating Gaussian field, we show that near criticality (where the field displays long-range spatial correlations) the spat...

The recent success of neural networks in natural language processing has drawn renewed attention to learning sequence-to-sequence (seq2seq) tasks. While there exists a rich literature that studies classification and regression tasks using solvable models of neural networks, seq2seq tasks have not yet been studied from this perspective. Here, we pro...

We study the nonreciprocal Cahn-Hilliard model with thermal noise as a prototypical example of a generic class of non-Hermitian stochastic field theories, analyzed in two companion papers [Suchanek, Kroy, and Loos, Phys. Rev. Lett. 131, 258302 (2023); Phys. Rev. E 108, 064123 (2023)]. Due to the nonreciprocal coupling between two field components,...

We study fluctuating field models with spontaneously emerging dynamical phases. We consider two typical transition scenarios associated with parity-time symmetry breaking: oscillatory instabilities and critical exceptional points. An analytical investigation of the low-noise regime reveals a drastic increase of the mesoscopic entropy production tow...

We study time-reversal symmetry breaking in non-Hermitian fluctuating field theories with conserved dynamics, comprising the mesoscopic descriptions of a wide range of nonequilibrium phenomena. They exhibit continuous parity-time (PT) symmetry-breaking phase transitions to dynamical phases. For two concrete transition scenarios, exclusive to non-He...

Adaptivity is a dynamical feature that is omnipresent in nature, socio-economics, and technology. For example, adaptive couplings appear in various real-world systems, such as the power grid, social, and neural networks, and they form the backbone of closed-loop control strategies and machine learning algorithms. In this article, we provide an inte...

We develop a theory for the stochastic thermodynamics of a probe coupled to a fluctuating medium with spatio-temporal correlations, described by a scalar field. For a Brownian particle dragged by a harmonic trap through a fluctuating Gaussian field, we show that near criticality the spatially-resolved heat flux develops an unexpected dipolar struct...

We study time-reversal symmetry breaking in non-Hermitian fluctuating field theories with conserved dynamics, comprising the mesoscopic descriptions of a wide range of nonequilibrium phenomena. They exhibit continuous parity-time (PT) symmetry breaking phase transitions to dynamical phases. For two concrete transition scenarios, exclusive to non-He...

We study a two-dimensional, nonreciprocal XY model, where each spin interacts only with its nearest neighbors in a certain angle around its current orientation, i.e., its “vision cone.” Using energetic arguments and Monte Carlo simulations, we show that a true long-range ordered phase emerges. A necessary ingredient is a configuration-dependent bon...

We study the nonreciprocal Cahn-Hilliard model with thermal noise as a prototypical example of a generic class of non-Hermitian stochastic field theories, analyzed in two companion papers [Suchanek, Kroy, Loos, ArXiv:2303.16701 (2023); Suchanek, Kroy, Loos, in preparation]. Due to the nonreciprocal coupling between two field components, the model i...

We study fluctuating field models with spontaneously emerging dynamical phases. We consider two typical transition scenarios, oscillatory instabilities and exceptional-point transitions associated with parity-time symmetry breaking. An analytical investigation of the low-noise limit reveals an unbounded increase of the mesoscopic entropy production...

We study the heat transfer between two nanoparticles held at different temperatures that interact through nonreciprocal forces, by combining molecular dynamics simulations with stochastic thermodynamics. Our simulations reveal that it is possible to construct nano refrigerators that generate a net heat transfer from a cold to a hot reservoir at the...

Adaptivity is a dynamical feature that is omnipresent in nature, socio-economics, and technology. For example, adaptive couplings appear in various real-world systems like the power grid, social, and neural networks, and they form the backbone of closed-loop control strategies and machine learning algorithms. In this article, we provide an interdis...

We study the heat transfer between two nanoparticles held at different temperatures that interact through nonreciprocal forces, by combining molecular dynamics simulations with stochastic thermodynamics. Our simulations reveal that it is possible to construct nano refrigerators that generate a net heat transfer from a cold to a hot reservoir at the...

We study a two-dimensional, nonreciprocal XY model, where each spin interacts only with its nearest neighbours in a certain angle around its current orientation, in analogy to a vision cone found in active systems. Using energetic arguments and Monte-Carlo simulations we demonstrate the emergence of a long-range ordered phase. A necessary ingredien...

The recent success of neural networks in machine translation and other fields has drawn renewed attention to learning sequence-to-sequence (seq2seq) tasks. While there exists a rich literature that studies classification and regression using solvable models of neural networks, learning seq2seq tasks is significantly less studied from this perspecti...

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...

Living many-body systems often exhibit scale-free collective behavior reminiscent of thermal critical phenomena. But their mutual interactions are inevitably retarded due to information processing and delayed actuation. We numerically investigate the consequences for the finite-size scaling in the Vicsek model of motile active matter. A growing del...

Finally, we introduce another theoretical framework employed in this thesis: stochastic thermodynamics. The latter is a rather young theory, which aims at a generalization of thermodynamic notions towards small-scale systems dominated by thermal fluctuations and towards nonequilibrium systems [2]. On this scale, individual fluctuating trajectories...

Finding thermodynamic notions for non-Markovian systems is a major problem. As a first step in this direction, we consider the heat rate \(\dot{Q}=\langle \delta q /\mathrm {d}t\rangle _\mathrm {ss}\) of nonlinear systems with discrete delay. This quantity can be calculated via well-established concepts from stochastic thermodynamics, in particular...

So far, we have discussed different approximations of the one-time probability density function, stemming from approaches based on the first member of the Fokker-Planck hierarchy. In particular, we have discussed the perturbation theory and the force-linearization closure (Chap. 7). While these approaches render quite accurate descriptions of the i...

While you are reading this thesis, at every instant of time countless particles of the surrounding air hit your skin due to their irregular thermal motion. There are of the order of \({\sim } 10^{23}\) molecules in every liter of air [1, 2].

In this chapter, we turn to the problem of finding (approximate) probabilistic solutions of systems with delay. In particular, we discuss an approximation scheme for the steady-state one-time PDF, which we have introduced in Ref. [1], called Force-linearization closure (FLC).

In this Chapter, we derive the FP hierarchy by using a Markovian embedding technique, which is inspired by the linear chain trick [3, 4, 5]. Markovian embeddings are already a well-established tool to treat stochastic systems with memory, for example in the context of generalized Langevin equations [6, 7, 8, 9, 10, 11]. The following considerations...

In this chapter, we will examine the infinite Fokker-Planck hierarchy. We will explicitly consider the higher members, which play a crucial role to understand the non-Markovian dynamics. Later in Chap. 6, we will present a new derivation of the FP description using a Markovian embedding technique [1, 2, 3, 4, 5, 6]. To better understand the technic...

We close with some comments putting the findings presented in this thesis into a broader perspective and giving an outlook on future research. We begin with formulating a few obvious follow-up questions and take a wider view towards the end.

In the preceding chapter, we have introduced the Langevin equation, which describes the random processes studied in this thesis on a stochastic level. For Markovian systems, it is well known that Fokker-Planck equations (FPE) provide a complementary way of description, on the probabilistic level. These are deterministic equations, whose solutions a...

In the last chapter, we have studied one component of the steady-state entropy balance, the medium entropy production and associated heat flow. While this investigation has already provided interesting insights, open questions remain. First, we observed that the mean heat rate can vanish at some specific, rare parameter values, despite the presence...

Stochastic processes with 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 nonlinear stochastic delay processes that obey fluctuation the...

Living many-body systems often exhibit scale-free collective behavior reminiscent of thermal critical phenomena. But their mutual interactions are inevitably retarded due to information processing and delayed actuation. We numerically investigate the consequences for the finite-size scaling in the Vicsek model of motile active matter. A growing del...

Many natural and artificial systems are subject to some sort of delay, which can be in the form of a single discrete delay or distributed over a range of times. Here, we discuss the impact of this distribution on (thermo-)dynamical properties of time-delayed stochastic systems. To this end, we study a simple classical model with white and colored n...

This paper is concerned with correlation functions of stochastic systems with memory, a prominent example being a molecule or colloid moving through a complex (e.g. viscoelastic) fluid environment. Analytical investigations of such systems based on non-Markovian stochastic equations are notoriously difficult. A common approximation is that of a sin...

The nonequilibrium behavior of nanoscopic and biological systems, which are typically strongly fluctuating, is a major focus of current research. Lately, much progress has been made in understanding such systems from a thermodynamic perspective. However, new theoretical challenges emerge when the fluctuating system is additionally subject to time d...

We study the thermodynamic properties induced by non-reciprocal interactions between stochastic degrees of freedom in time- and space-continuous systems. We show that, under fairly general conditions, non-reciprocal coupling alone implies a steady energy flow through the system, i.e., non-equilibrium. Projecting out the non-reciprocally coupled deg...

This paper is concerned with correlation functions of stochastic systems with memory, a prominent example being a molecule or colloid moving through a complex (e.g., viscoelastic) fluid environment. Analytical investigations of such systems based on non-Markovian stochastic equations are notoriously difficult. A common approximation is that of a si...

Understanding nonequilibrium systems and the consequences of irreversibility for the system's behavior as compared to the equilibrium case, is a fundamental question in statistical physics. Here, we investigate two types of nonequilbrium phase transitions, a second-order and an infinite-order phase transition, in a prototypical q-state vector Potts...

Understanding nonequilibrium systems and the consequences of irreversibility for the system's behavior as compared to the equilibrium case, is a fundamental question in statistical physics. Here, we investigate two types of nonequilibrium phase transitions, a second-order and an infinite-order phase transition, in a prototypical q-state vector Pott...

We study the thermodynamic properties induced by non-reciprocal interactions between stochastic degrees of freedom in time- and space-continuous systems. We show that, under fairly general conditions, non-reciprocal coupling alone implies a steady energy flow through the system, i.e., non-equilibrium. Projecting out the non-reciprocally coupled deg...

In addition to the ever-present random fluctuations due to noise, many systems in biology, physics and technology involve discrete time delay, stemming, e.g., from finite information transmission times. The combination of noise and delay yields non-Markovian dynamics describable by time-nonlocal Langevin equations with a delta-peaked memory kernel....

We show that memory, feedback, and activity are all describable by the same unifying concept, that is non-reciprocal (NR) coupling. We demonstrate that characteristic thermodynamic features of these intrinsically nonequilibrium systems are reproduced by low-dimensional Markovian networks with NR coupling, which we establish as minimal models for su...

For stochastic systems with discrete time delay, the Fokker–Planck equation (FPE) of the one-time probability density function (PDF) does not provide a complete, self-contained probabilistic description. It explicitly involves the two-time PDF, and represents, in fact, only the first member of an infinite hierarchy. We here introduce a new approach...

For stochastic systems with discrete time delay, the Fokker-Planck equation (FPE) of the one-time probability density function (PDF) does not provide a complete, self-contained probabilistic description, as it explicitly involves the two-time PDF. We here introduce a new approach to find a Fokker-Planck description by using a Markovian embedding te...

For stochastic systems with discrete time delay, the Fokker-Planck equation (FPE) of the one-time probability density function (PDF) does not provide a complete, self-contained probabilistic description, as it explicitly involves the two-time PDF. We here introduce a new approach to find a Fokker-Planck description by using a Markovian embedding te...

The thermodynamics of stochastic non-Markovian systems is still widely unexplored. We present an analytical approach for the net steady-state heat flux in nonlinear overdamped systems subject to a continuous feedback force with a discrete time delay. We show that the feedback inevitably leads to a finite heat flow even for vanishingly small delay t...

This paper is concerned with the Fokker-Planck (FP) description of classical stochastic systems with discrete time delay. The non-Markovian character of the corresponding Langevin dynamics naturally leads to a coupled infinite hierarchy of FP equations for the various $n$-time joint distribution functions. Here we present a novel approach to close...

We investigate partially coherent and partially incoherent patterns (chimera states) in networks of Stuart-Landau oscillators with symmetry-breaking coupling. In particular, we study two types of chimera states, amplitude chimeras and chimera death, under the influence of time delay and noise. We find that amplitude chimeras are long-living transie...

We review recent work on feedback control of one-dimensional colloidal systems, both with instantaneous feedback and with time delay. The feedback schemes are based on measurement of the average particle position, a natural control target for an ensemble of colloidal particles, and the systems are investigated via the Fokker-Planck equation for ove...

We investigate amplitude chimera states in nonlinear dynamical networks, which consist of coexisting domains of synchronized and desynchronized dynamics. In particular, we analyze the role of time delay and stochasticity for these synchronization-desynchronization patterns. We address the question of robustness and control of amplitude chimera stat...

We review recent work on feedback control of one-dimensional colloidal systems, both with instantaneous feedback and with time delay. The feedback schemes are based on measurement of the average particle position, a natural control target for an ensemble of colloidal particles, and the systems are investigated via the Fokker-Planck equation for ove...

We investigate two types of chimera states, i.e., patterns consisting of coexisting spatially separated domains with coherent and incoherent dynamics, in ring networks of Stuart-Landau oscillators with symmetry-breaking coupling, under the influence of noise. Amplitude chimeras are characterized by temporally periodic dynamics throughout the whole...

In a network of nonlocally coupled Stuart-Landau oscillators with symmetry-breaking coupling, we study numerically, and explain analytically, a family of inhomogeneous steady states (oscillation death). They exhibit multi-cluster patterns, depending on the cluster distribution prescribed by the initial conditions. Besides stable oscillation death,...

Based on the Fokker-Planck equation we investigate the transport of an overdamped colloidal particle in a static, asymmetric periodic potential supplemented by a time-dependent, delayed feedback force, $F_{\mathrm{fc}}$. For a given time $t$, $F_\mathrm{fc}$ depends on the status of the system at a previous time $t-\tau_\mathrm{D}$, with $\tau_\mat...