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Motivated by the need for precise, energy-efficient, and experimentally realistic quantum control protocols, we investigate the thermodynamic cost of performing quantum step-equilibration processes under the influence of classical…

Quantum Physics · Physics 2026-05-07 Theodore McKeever , Harry J. D. Miller , Ahsan Nazir

Stochastic Spatio-Temporal processes are prevalent across domains ranging from modeling of plasma to the turbulence in fluids to the wave function of quantum systems. This letter studies a measure-theoretic description of such systems by…

Optimization and Control · Mathematics 2021-05-25 George I. Boutselis , Ethan N. Evans , Marcus A. Pereira , Evangelos A. Theodorou

In the real world, one almost never knows the parameters of a thermodynamic process to infinite precision. Reflecting this, here we investigate how to extend stochastic thermodynamics to systems with uncertain parameters, including…

Statistical Mechanics · Physics 2021-03-17 Jan Korbel , David H. Wolpert

Performing thermodynamic tasks within finite time while minimizing thermodynamic costs is a central challenge in stochastic thermodynamics. Here, we develop a unified framework for optimizing the thermodynamic cost of performing various…

Statistical Mechanics · Physics 2025-09-16 Kaito Tojo , Rihito Nagase , Ken Funo , Takahiro Sagawa

We consider optimization of the average entropy production in inhomogeneous temperature environments within the framework of stochastic thermodynamics. For systems modeled by Langevin equations (e.g. a colloidal particle in a heat bath) it…

Statistical Mechanics · Physics 2013-03-14 Stefano Bo , Erik Aurell , Ralf Eichhorn , Antonio Celani

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…

Statistical Mechanics · Physics 2014-05-28 Viktor Holubec

The optimal control of passive systems in equilibrium typically favours quasistatic (infinite-time) protocols. We show that a breakdown of quasistatic optimality occurs when the controller itself is dissipative. Concretely, we study a…

Statistical Mechanics · Physics 2026-05-08 Luca Cocconi , Henry Alston , Thibault Bertrand

Stochastic thermodynamics is a framework for describing non-equilibrium processes at the level of fluctuating trajectories, where the state of a system evolves as a stochastic time series, allowing thermodynamic quantities such as work,…

A stochastic procedure is developed which allows one to express Pontryagin's maximum principle for dissipative quantum system solely in terms of stochastic wave functions. Time-optimal controls can be efficiently computed without computing…

Quantum Physics · Physics 2020-11-09 Chungwei Lin , Dries Sels , Yanting Ma , Yebin Wang

Controlling the evolution of nonequilibrium systems to minimize dissipated heat or work is a key goal for designing nanodevices, both in nanotechnology and biology. Progress in computing optimal protocols has thus far been limited to either…

Computational Physics · Physics 2022-01-04 Megan C. Engel , Jamie A. Smith , Michael P. Brenner

Stochastic resetting is a driving mechanism that is known to minimize the first passage time to reach a target, at the cost of energy expenditure. The choice of the physical implementation of each resetting event determines the tradeoff…

Statistical Mechanics · Physics 2025-07-29 Rémi Goerlich , Kristian Stølevik Olsen , Hartmut Löwen , Yael Roichman

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…

Statistical Mechanics · Physics 2018-03-23 Yongxin Chen , Tryphon Georgiou , Allen Tannenbaum

A fundamental problem in modern thermodynamics is how a molecular-scale machine performs useful work, while operating away from thermal equilibrium without excessive dissipation. To this end, we derive a friction tensor that induces a…

Statistical Mechanics · Physics 2012-05-09 David A. Sivak , Gavin E. Crooks

Differential geometry offers a powerful framework for optimising and characterising finite-time thermodynamic processes, both classical and quantum. Here, we start by a pedagogical introduction to the notion of thermodynamic length. We…

Quantum Physics · Physics 2021-08-31 Paolo Abiuso , Harry J. D. Miller , Martí Perarnau-Llobet , Matteo Scandi

The tradeoff relation between speed and cost is a central issue in designing fast and efficient information processing devices. We derive an achievable bound on thermodynamic cost for obtaining information through finite-time…

Statistical Mechanics · Physics 2024-05-16 Rihito Nagase , Takahiro Sagawa

In these lecture notes, the basic principles of stochastic thermodynamics are developed starting with a closed system in contact with a heat bath. A trajectory undergoes Markovian transitions between observable meso-states that correspond…

Statistical Mechanics · Physics 2018-06-13 Udo Seifert

The study of stochastic thermodynamic machines is one of the main topics in nonequilibrium thermodynamics. In this study, within the framework of Fokker-Planck equation, and using the method of characteristics of partial differential…

Statistical Mechanics · Physics 2020-04-03 Yunxin Zhang

What are the fundamental limitations placed by the laws of thermodynamics on the energy expenditure needed to carry out a given task in a nonequilibrium environment in finite time? In this thesis, we investigate "optimal nonequilibrium…

Statistical Mechanics · Physics 2025-09-30 Adrianne Zhong

The design of efficient quantum information processing will rely on optimal nonequilibrium transitions of driven quantum systems. Building on a recently-developed geometric framework for computing optimal protocols for classical systems…

Statistical Mechanics · Physics 2015-10-28 Patrick R. Zulkowski , Michael R. DeWeese

The goal of thermodynamic optimal control theory is to find protocols to change the state of a system from an initial to a desired final distribution, within a finite time, with the least possible expenditure of work. The optimal protocol…

Statistical Mechanics · Physics 2025-12-18 Daan Mulder , Thomas E. Ouldridge , Pieter Rein ten Wolde