Related papers: Limited-control optimal protocols arbitrarily far …
The investigation of optimal processes has a long history in the field of thermodynamics. It is well known that finite-time processes that minimize dissipation often exhibit discontinuities. We use a combination of numerical and analytical…
This paper considers the relaxed version of the transport problem for general nonlinear control systems, where the objective is to design time-varying feedback laws that transport a given initial probability measure to a target probability…
Thermodynamics of small systems has become an important field of statistical physics. They are driven out of equilibrium by a control, and the question is naturally posed how such a control can be optimized. We show that optimization…
This paper develops a unified methodology for probabilistic analysis and optimal control design for jump diffusion processes defined by polynomials. For such systems, the evolution of the moments of the state can be described via a system…
We investigate a stochastic heat engine based on an over-damped particle diffusing on the positive real axis in an externally driven time-periodic log-harmonic potential. The periodic driving is composed of two isothermal and two adiabatic…
The optimal protocols for the irreversible work achieve their maximum usefulness if their work fluctuations are the smallest ones. In this work, for classical and isothermal processes subjected to finite-time and weak drivings, I show that…
We consider damped stochastic systems in a controlled (time-varying) quadratic potential and study their transition between specified Gibbs-equilibria states in finite time. By the second law of thermodynamics, the minimum amount of work…
Quantifying energy flows at nanometer scales promises to guide future research in a variety of disciplines, from microscopic control and manipulation, to autonomously operating molecular machines. A general understanding of the…
In this paper we study the optimal control of a parabolic initial-boundary value problem of viscous Cahn-Hilliard type with zero Neumann boundary conditions. Phase field systems of this type govern the evolution of diffusive phase…
The realization of efficient micro-machines built from active matter requires precise thermodynamic control far from equilibrium. Despite theoretical progress, the focus on single-parameter driving, coupled with strict theoretical…
This paper introduces a novel approach to the optimal control of linear discrete-time systems subject to bounded disturbances. Our approach is based on the newly established duality between ellipsoidal approximations of reachable and hardly…
We investigate different turnpike phenomena of generalized discrete-time stochastic linear-quadratic optimal control problems. Our analysis is based on a novel strict dissipativity notion for such problems, in which a stationary stochastic…
We present an analysis of the work performed on a system of interest that is kept thermally isolated during the switching of a control parameter. We show that there exists, for a certain class of systems, a finite-time family of switching…
Extracting useful work from quantum systems is a fundamental problem in quantum thermodynamics. In scenarios where rapid protocols are desired -- whether due to practical constraints or deliberate design choices -- a fundamental trade-off…
In this article, we discuss two algorithms tailored to discrete-time deterministic finite-horizon nonlinear optimal control problems or so-called deterministic trajectory optimization problems. Both algorithms can be derived from an…
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…
Driven barrier crossings are pervasive in optical-trapping experiments and steered molecular-dynamics simulations. Despite the high fidelity of control, the freedom in the choice of driving protocol is rarely exploited to improve…
A system's configurational state can be manipulated using dynamic variation of control parameters, such as temperature, pressure, or magnetic field; for finite-duration driving, excess work is required above the equilibrium free-energy…
This paper presents a novel method to synthesize stochastic control Lyapunov functions for a class of nonlinear, stochastic control systems. In this work, the classical nonlinear Hamilton-Jacobi-Bellman partial differential equation is…
We look into the minimisation of the connection time between non-equilibrium steady states. As a prototypical example of an intrinsically non-equilibrium system, a driven granular gas is considered. For time-independent driving, its natural…