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A generalized version of the Maximum Work Theorem is valid when the system is initially not at thermal equilibrium. In this work, we initially study the fraction of trajectories that violate this generalized theorem for a two simple…

Statistical Mechanics · Physics 2017-09-15 Sourabh Lahiri , Arun M. Jayannavar , Anupam Kundu

Single-molecule experiments have found near-perfect thermodynamic efficiency in the rotary motor F1-ATP synthase. To help elucidate the principles underlying nonequilibrium energetic efficiency in such stochastic machines, we investigate…

Statistical Mechanics · Physics 2019-09-05 Joseph N. E. Lucero , Aliakbar Mehdizadeh , David A. Sivak

Adiabaticity is a cornerstone of many promising approaches to quantum control, computing, and simulation. In practice, however, there is always a trade-off. Although the deleterious effects of noise can be diminished by running a control…

Quantum Physics · Physics 2025-06-23 Pavel Zhelnin , Lucas Johns , Carlos A. Argüelles

The development of efficient artificial nanodevices poses challenges which are of fundamental and technological nature. Recent progress has been made in the context of finite-time thermodynamics. A central question in finite-time…

Statistical Mechanics · Physics 2014-03-18 Mario Einax

A positive rate of entropy production at steady state is a distinctive feature of truly non-equilibrium processes. Exact results, while being often limited to simple models, offer a unique opportunity to explore the thermodynamic features…

Statistical Mechanics · Physics 2022-06-29 Henry Alston , Luca Cocconi , Thibault Bertrand

We propose a general framework to study transformations that drive an underdamped Brownian particle in contact with a thermal bath from an equilibrium state to a new one in an arbitrarily short time. To this end, we make use of a time and…

Statistical Mechanics · Physics 2019-01-21 Marie Chupeau , Sergio Ciliberto , David Guéry-Odelin , Emmanuel Trizac

The minimal work principle states that work done on a thermally isolated equilibrium system is minimal for adiabatically slow (reversible) realization of a given process. This principle, one of the formulations of the second law, is studied…

Statistical Mechanics · Physics 2009-11-10 A. E. Allahverdyan , Th. M. Nieuwenhuizen

A central goal of thermodynamics is to identify optimal processes during which the least amount of energy is dissipated into the environment. Generally, even for simple systems, such as the parametric harmonic oscillator, optimal control…

Statistical Mechanics · Physics 2018-10-11 Marcus V. S. Bonança , Sebastian Deffner

Nonequilibrium physics encompasses a broad range of natural and synthetic small-scale systems. Optimizing transitions of such systems will be crucial for the development of nanoscale technologies and may reveal the physical principles…

Statistical Mechanics · Physics 2015-09-23 Patrick R. Zulkowski , Michael R. DeWeese

Physical systems driven away from equilibrium by an external controller dissipate heat to the environment; the excess entropy production in the thermal reservoir can be interpreted as a "cost" to transform the system in a finite time. The…

Statistical Mechanics · Physics 2024-12-31 Jérémie Klinger , Grant M. Rotskoff

Constructing optimal thermodynamic processes in quantum systems relies on managing the balance between the average excess work and its stochastic fluctuations. Recently it has been shown that two different quantum generalisations of…

Quantum Physics · Physics 2021-12-06 Mohammad Mehboudi , Harry J. D. Miller

We analyze the control of the motion of a charged particle by means of an external electric field. The system is constrained to move along a given direction. The goal of the control is to change the speed of the particle in a fixed time…

Optimization and Control · Mathematics 2020-01-22 V. Martikyan , D. Guéry-Odelin , D. Sugny

Stochastic thermodynamics as reviewed here systematically provides a framework for extending the notions of classical thermodynamics like work, heat and entropy production to the level of individual trajectories of well-defined…

Statistical Mechanics · Physics 2015-06-05 Udo Seifert

We generalize to non equilibrium states Onsager's minimum dissipation principle. We also interpret this principle and some previous results in terms of optimal control theory. Entropy production plays the role of the cost necessary to drive…

Statistical Mechanics · Physics 2015-12-18 L. Bertini , A. De Sole , D. Gabrielli , G. Jona-Lasinio , C. Landim

We study the problem of state transition on a finite time interval with minimal energy supply for linear port-Hamiltonian systems. While the cost functional of minimal energy supply is intrinsic to the port-Hamiltonian structure, the…

Optimization and Control · Mathematics 2023-11-21 Timm Faulwasser , Jonas Kirchhoff , Volker Mehrmann , Friedrich Philipp , Manuel Schaller , Karl Worthmann

Many techniques originally developed in the context of deterministic control theory have been recently applied to the quest for optimal protocols in stochastic processes. Given a system subject to environmental fluctuations, one may ask…

Statistical Mechanics · Physics 2025-01-15 Dario Lucente , Alessandro Manacorda , Andrea Plati , Alessandro Sarracino , Marco Baldovin

People are well aware that, inherently, certain small-scale nonchaotic particle movements are not governed by thermodynamics. Usually, such phenomena are studied by kinetic theory and their energy properties are considered "trivial". In…

Statistical Mechanics · Physics 2025-08-05 Yu Qiao , Zhaoru Shang

We consider irreversible and coupled reversible-irreversible nonlinear port-Hamiltonian systems and the respective sets of thermodynamic equilibria. In particular, we are concerned with optimal state transitions and output stabilization on…

Optimization and Control · Mathematics 2024-10-08 Friedrich Philipp , Manuel Schaller , Karl Worthmann , Timm Faulwasser , Bernhard Maschke

We study adaptive control of classical ergodic Hamiltonian systems, where the controlling parameter varies slowly in time and is influenced by system's state (feedback). An effective adiabatic description is obtained for slow variables of…

Statistical Mechanics · Physics 2009-11-13 A. E. Allahverdyan , D. B. Saakian

In this work, we study the nonequilibrium statistical properties of the relaxation dynamics of a nanoparticle trapped in a harmonic potential. We report an exact time-dependent analytical solution to the Langevin dynamics that arises from…

Statistical Mechanics · Physics 2016-11-23 Domingos S. P. Salazar , Sérgio A. Lira