Stochastic thermodynamics as reviewed here systematically provides a framework for extending the notions of classical thermodynamics such as work, heat and entropy production to the level of individual trajectories of well-defined non-equilibrium ensembles. It applies whenever a non-equilibrium process is still coupled to one (or several) heat bath(s) of constant temperature. Paradigmatic systems are single colloidal particles in time-dependent laser traps, polymers in external flow, enzymes and molecular motors in single molecule assays, small biochemical networks and thermoelectric devices involving single electron transport. For such systems, a first-law like energy balance can be identified along fluctuating trajectories. For a basic Markovian dynamics implemented either on the continuum level with Langevin equations or on a discrete set of states as a master equation, thermodynamic consistency imposes a local-detailed balance constraint on noise and rates, respectively. Various integral and detailed fluctuation theorems, which are derived here in a unifying approach from one master theorem, constrain the probability distributions for work, heat and entropy production depending on the nature of the system and the choice of non-equilibrium conditions. For non-equilibrium steady states, particularly strong results hold like a generalized fluctuation–dissipation theorem involving entropy production. Ramifications and applications of these concepts include optimal driving between specified states in finite time, the role of measurement-based feedback processes and the relation between dissipation and irreversibility. Efficiency and, in particular, efficiency at maximum power can be discussed systematically beyond the linear response regime for two classes of molecular machines, isothermal ones such as molecular motors, and heat engines such as thermoelectric devices, using a common framework based on a cycle decomposition of entropy production. (Some figures may appear in colour only in the online journal) This article was invited by Erwin Frey.

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Stochastic thermodynamics, fluctuation theorems and molecular machines

Jets, ie collimated streams of matter, occur from the microscale up to the large-scale structure of the universe Our focus will be mostly on surface tension effects, which result from the cohesive properties of liquids Paradoxically, cohesive forces promote the breakup of jets, widely encountered in nature, technology and basic science, for example in nuclear fission, DNA sampling, medical diagnostics, sprays, agricultural irrigation and jet engine technology Liquid jets thus serve as a paradigm for free-surface motion, hydrodynamic instability and singularity formation leading to drop breakup In addition to their practical usefulness, jets are an ideal probe for liquid properties, such as surface tension, viscosity or non-Newtonian rheology They also arise from the last but one topology change of liquid masses bursting into sprays Jet dynamics are sensitive to the turbulent or thermal excitation of the fluid, as well as to the surrounding gas or fluid medium The aim of this review is to provide a unified description of the fundamental and the technological aspects of these subjects

Physics of liquid jets

In systems possessing spatial or dynamical symmetry breaking, Brownian motion combined with unbiased external input signals, deterministic and random alike, can assist directed motion of particles at submicron scales. In such cases, one speaks of ``Brownian motors.'' In this review the constructive role of Brownian motion is exemplified for various physical and technological setups, which are inspired by the cellular molecular machinery: the working principles and characteristics of stylized devices are discussed to show how fluctuations, either thermal or extrinsic, can be used to control diffusive particle transport. Recent experimental demonstrations of this concept are surveyed with particular attention to transport in artificial, i.e., nonbiological, nanopores, lithographic tracks, and optical traps, where single-particle currents were first measured. Much emphasis is given to two- and three-dimensional devices containing many interacting particles of one or more species; for this class of artificial motors, noise rectification results also from the interplay of particle Brownian motion and geometric constraints. Recently, selective control and optimization of the transport of interacting colloidal particles and magnetic vortices have been successfully achieved, thus leading to the new generation of microfluidic and superconducting devices presented here. The field has recently been enriched with impressive experimental achievements in building artificial Brownian motor devices that even operate within the quantum domain by harvesting quantum Brownian motion. Sundry akin topics include activities aimed at noise-assisted shuttling other degrees of freedom such as charge, spin, or even heat and the assembly of chemical synthetic molecular motors. This review ends with a perspective for future pathways and potential new applications.

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Artificial Brownian motors: Controlling transport on the nanoscale

The cortex is a complex system, characterized by its dynamics and architecture, which underlie many functions such as action, perception, learning, language, and cognition Its structural architecture has been studied for more than a hundred years; however, its dynamics have been addressed much less thoroughly In this paper, we review and integrate, in a unifying framework, a variety of computational approaches that have been used to characterize the dynamics of the cortex, as evidenced at different levels of measurement Computational models at different space-time scales help us understand the fundamental mechanisms that underpin neural processes and relate these processes to neuroscience data Modeling at the single neuron level is necessary because this is the level at which information is exchanged between the computing elements of the brain; the neurons Mesoscopic models tell us how neural elements interact to yield emergent behavior at the level of microcolumns and cortical columns Macroscopic models can inform us about whole brain dynamics and interactions between large-scale neural systems such as cortical regions, the thalamus, and brain stem Each level of description relates uniquely to neuroscience data, from single-unit recordings, through local field potentials to functional magnetic resonance imaging (fMRI), electroencephalogram (EEG), and magnetoencephalogram (MEG) Models of the cortex can establish which types of large-scale neuronal networks can perform computations and characterize their emergent properties Mean-field and related formulations of dynamics also play an essential and complementary role as forward models that can be inverted given empirical data This makes dynamic models critical in integrating theory and experiments We argue that elaborating principled and informed models is a prerequisite for grounding empirical neuroscience in a cogent theoretical framework, commensurate with the achievements in the physical sciences

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The Dynamic Brain: From Spiking Neurons to Neural Masses and Cortical Fields

Normalizing flows provide a general mechanism for defining expressive probability distributions, only requiring the specification of a (usually simple) base distribution and a series of bijective transformations. There has been much recent work on normalizing flows, ranging from improving their expressive power to expanding their application. We believe the field has now matured and is in need of a unified perspective. In this review, we attempt to provide such a perspective by describing flows through the lens of probabilistic modeling and inference. We place special emphasis on the fundamental principles of flow design, and discuss foundational topics such as expressive power and computational trade-offs. We also broaden the conceptual framing of flows by relating them to more general probability transformations. Lastly, we summarize the use of flows for tasks such as generative modeling, approximate inference, and supervised learning.

Normalizing Flows for Probabilistic Modeling and Inference

The linear time invariant (LTI) observer-based discrete-time sliding-mode control problem is considered for a robust tracking of higher-order dynamic delay-time systems. Here, Luenberger observer is used for estimation of system states as all states are not available for measurement. Sliding surface is selected based on output feedback and observer states to realize the sliding-mode control. Observer and controller parameters are tabulated by pole placement strategy. The performance of proposed control is improved with dual tuning parameter in terms of settling time and control effort. Finally, non-oscillatory, oscillatory, integrating, and non-minimum phase systems with delay-time examples are implemented with numerical simulations to demonstrate the validity of the proposed control method.

Observer-based discrete-time sliding-mode control for higher-order dynamic delay-time system

In this paper, continuous-time sliding mode control based on the recently developed inertial delay control is extended to the discrete-time case. A notable feature of the proposed control is that it affords control over the magnitude of the quasi-sliding for a given sampling period. The use of the δ-operator in conjunction with a new sliding mode condition derived in this paper, enables complete and seamless unification of the sliding condition, control law and the underlying inertial delay control.

Robust control design using discrete sliding mode control for uncertain systems

Abstract This article contributes to handling the Non-Minimum Phase (NMP) system with time delay in the existence of uncertainty and disturbances. The series cascade control scheme is used to overcome such problems. The secondary loop architecture in a series cascade scheme is formulated in the Internal Model Control (IMC) framework. The tuning of fractional-filter via a delayed version of Bodes’ ideal transfer function approach of primary loop controller in a series cascade arrangement shows the novelty of this work. The primary loop controller is designed in the IMC framework after accountability of inverse response and dead-time compensator. Furthermore, Particle Swarm Optimization (PSO) is adapted to accomplish the optimal value of controller settings. The Riemann sheet principle is used to determine stability. The sensitivity investigation is performed to know the robustness of the offered controller. For the effectiveness of the suggested scheme, two case studies are revealed in this paper.

Hiren G. Patel

Papers

Observer-based discrete-time sliding-mode control for higher-order dynamic delay-time system

Robust control design using discrete sliding mode control for uncertain systems

Modified optimal series cascade control for non-minimum phase system