Linear response theory and causation detection

Slides

Detecting and quantifying causal links between different elements of a complex system, i.e. studying whether and how much the behavior of a given component affects the others, is a problem of primary importance in many fields of science. The task is particularly challenging when the observer cannot actively perturb the state of the system, and one can only rely on the analysis of measured correlations and related quantities.

In this talk the use of response theory to unveil causation is discussed. Under suitable conditions, the generalized Fluctuation-Dissipation Relation provides a handy way to infer the structure of the causal links in a complex dynamics. The markovianity of the system is shown to be a crucial condition, which can however be relaxed in the presence of large time-scale separation between the observed dynamics and the external forcing. Some recent results, based on the application of the above ideas to paleoclimatic data series, are presented and discussed.

Temperature inversion in a non-homogeneous two-component collisionless plasma

Slides

Numerical simulations of simple toy models have recently shown that when a long-range-interacting system is brought out of thermal equilibrium by a violent injection of energy, it relaxes towards a nonthermal quasi-stationary state in which the temperature profile presents a gradient opposite to that of the spatial density (usually referred to as ”temperature inversion”). Temperature inversions do occur in some astrophysical contexts, and especially in the atmosphere of the Sun. The inner region of the latter is a dense plasma in thermal equilibrium at a temperature less than 10000 K, while the outer atmosphere (the corona) is made of a less dense but much warmer collisionless plasma reaching temperatures of 1-2 millions K. Being at a lower temperature, the inner regions of the solar atmosphere cannot directly heat the corona. Understanding how can the solar corona reach such high temperatures is a fundamental unsolved problem of solar physics and more generally plasma physics, and it is known as the coronal heating problem. We shall present a new kinetic model of a two-component collisionless plasma confined in a semicircular tube (mimicking the so-called coronal loop structures) in contact with a thermal boundary, representing the inner layers of the atmosphere. We will show that when energy is injected into the loop at the thermal boundary by means of impulsive perturbations, the system evolves towards a non-equilibrium quasi-stationary state with temperature inversion for both the species (ions and electrons).

Generalized Density Profiles in Single-File Systems

Single-file transport, where particles diffuse in narrow channels while not overtaking each other, is a fundamental model for the tracer subdiffusion observed in confined systems, such as zeolites or carbon nanotubes. This anomalous behavior originates from strong bath-tracer correlations in 1D, which have however remained elusive, because they involve an infinite hierarchy of equations.

For the Symmetric Exclusion Process, a paradigmatic model of single-file diffusion, this hierarchy of equations can in fact be broken, and the bath-tracer correlations satisfy a closed equation, which can be solved. I will suggest that this equation appears as a novel tool for interacting particle systems, since it also applies to out-of equilibrium situations, other observables and other representative single-file systems.

Power and efficiency of thermodynamic engines: energy harvesting from anisotropic fluctuations

We discuss principles that underlie power transduction in thermodynamic systems that are subject to thermal fluctuations, and we will focus on how anisotropy in thermal fluctuations (chemical, electrical potential, and so on) allows generation of power in engineered and physical processes. We will present specific embodiments of pertinent controlled power-generating mechanisms. Our theme follows a long line of developments, from classical and non-equilibrium thermodynamics, onto recent formalisms that aim to quantify precisely such finite-time thermodynamic transitions and power generation.

The talk is based on joint works with Rui Fu (UCI), Olga Movilla (UCI), Amir Taghvaei (UCI) and Yongxin Chen (GaTech). Research funding by NSF and AFOSR is gratefully acknowledged.

Gravitational clustering in cosmology

Slides

I will give a brief overview of the description of the evolution under their self-gravity of small initial fluctuations in an expanding universe. In standard cosmologies the regime of interest, where the dynamics is non-linear, can be well approximated in the Newtonian limit. A central problem is then to determine how clustering statistics (as a function of time) depend on initial conditions and expansion history. I will describe how this problem can be addressed using a simplified family of so-called scale-free cosmologies, which are characterized by a simple scaling behavior of the clustering. I describe highly precise results for clustering statistics obtained recently from enormous numerical simulations of these models, and explain how the dependence of statistics in standard type cosmologies on initial conditions can be modeled accurately using them.

Long-range interacting systems in the unconstrained ensemble

Slides

The unconstrained ensemble describes completely open systems whose control parameters are the chemical potential, pressure and temperature. For macroscopic systems with short-range interactions, thermodynamics prevents the simultaneous use of these intensive variables as control parameters, because they are not independent and cannot account for the system size. When the range of the interactions is comparable with the size of the system, however, these variables are not truly intensive and may become independent, so equilibrium states defined by the values of these parameters may exist. The independence in this set of variables is directly related to the fact that the system is non-additive. After reviewing the thermodynamics of non-additive systems, in the talk we consider some examples of systems with long-range interactions that reach equilibrium under completely open conditions. We also present a Monte Carlo algorithm to perform simulations in the unconstrained ensemble and complement the discussion of the examples with simulations.

Classical speed limit and tight finite-time Landauer's bound

Slides

Landauer's bound is the minimum thermodynamic cost for erasing one bit of information. As this bound is achievable only for quasistatic processes, finite-time operation incurs additional energetic costs. We find a “tight” finite-time Landauer's bound by establishing a general form of the classical speed limit. This tight bound well captures the divergent behavior associated with the additional cost of a highly irreversible process, which scales differently from a nearly irreversible process. We demonstrate the validity of this bound via discrete one-bit and coarse-grained bit systems. Our work implies that more heat dissipation than expected occurs during high-speed irreversible computation.

Ref: J. S. Lee, S. Lee, H. Kwon, and H. Park, arXiv:2204.07388

Non-equilibrium dynamics of particles coupled to fluctuating fields

(with Andrea Gambassi^1,2, Davide Venturelli^1,2, Sarah Loos^3,4, Edgar Roldan^3, and Jonas Jager^5)

1 SISSA Trieste

2 INFN, Sezione di Trieste

3 ICTP Trieste

4 Univ. Cambridge

5 Imperial College London

I present three related projects concerned with the non-equilibrium dynamics and thermodynamics of particles coupled to fluctuating fields. In each of them, a particle is coupled to a heat bath as well as a critical or near-critical (order parameter) field modelling complex environments with spatiotemporal correlations. The coupling is assumed to be weak and treated using perturbation theory. Because of the correlations in the field, the particle's dynamics are non-Markovian and display a rich phenomenology.

In Part I, I discuss the case of an overdamped Brownian particle linearly coupled to a surrounding fluctuating field. This microrheological model can be applied to study colloidal transport in disordered media, such as in biological cells or tissues, or spin glasses. I outline strengths and limitations of a field-theoretic (and diagrammatic) approach in studying the quenched dynamics of a newly inserted particle, and also discuss the case of self-interacting fields. Further, I describe how the tracer particle's dynamics can be used to infer critical properties of the field, which is useful in situations where the field itself is difficult to observe experimentally. I conclude with some preliminary results on fields which are themselves out-of-equilibirum.

In Part II, I present a similar model of an impurity coupled quadratically to a surrounding field. In contrast to the previous part, the particle follows Newtonian (instead of overdamped) dynamics. This model is inspired by the study of polarons in Bose-Einstein condensates. We approach this problem by an effective action approach which we compute to leading perturbative order. I discuss the differences and similarities to the overdamped and linear case introduced before as well as some possible future applications to driven-dissipative condensates.

In Part III, I show some recent result on the stochastic energetics of a tracer particle which is dragged, for instance by an optical tweezer, through a fluctuating field. Thermodynamically, the energy which flows into the system via the dragging needs to be dissipated into both the surrounding heat bath as well as the field. Combining stochastic thermodynamics and perturbative field theory, we perturbatively calculate the average power and the spatially resolved average energy dissipation in the non-equilibrium steady state.