Entropic equality for worst-case work at any protocol speed

We study the thermodynamic cost associated with the erasure of one bit of information over a finite amount of time. We present a general framework for minimizing the average work required when full control of a system's microstates is possible. In addition to exact numerical results, we find simple bounds proportional to the variance of the microscopic distribution associated with the state of the bit. In the short-time limit, we get a closed expression for the minimum averag...

We present a protocol for the study of the dynamics and thermodynamics of quantum systems strongly coupled to a bath and subject to an external modulation. Our protocol quantifies the evolution of the system-bath composite by expanding the full density matrix as a series in the powers of the modulation rate, from which the functional form of work, heat and entropy rates can be obtained. Under slow driving, thermodynamic laws are established. The entropy production rate is pos...

This document presents the contents of three lectures delivered by the author at the Erd\H{o}s Center School ``Optimal Transport on Quantum Structures'', Septemer 19-23, 2022 in Budapest, Hungary. It presents a fairly self contained account of an active topic of current research, and this account should be accessible to most graduate students, as befits lectures for a school. The main results are known, but there a number of new proofs and some new results.

Recently proposed information-exploiting systems designed to extract work from a single heat bath utilize temporal correlations on an input tape. We study how enforcing time-continuous dynamics, which is necessary to ensure the device is physically realizable, constrains possible designs and drastically diminishes efficiency. We show that these problems can be circumvented by means of applying an external, time-varying protocol. This turns the device from a "passive", free-ru...

We discuss a simple but experimentally realistic model system, a single-electron box (SEB), where common fluctuation relations can be tested for driven electronic transitions. We show analytically that when the electron system on the SEB island is overheated by the control parameter (gate voltage) drive, the common fluctuation relation (Jarzynski equality) is only approximately valid due to dissipated heat even when the system starts at thermal equilibrium and returns to it a...

We show that the maximum extractable work (ergotropy) from a quantum many-body system is constrained by local athermality of an initial state and local entropy decrease brought about by quantum operations. The obtained universal bound on ergotropy implies that the eigenstate thermalization hypothesis prohibits work extraction from energy eigenstates by means of finite-time unitary operations. This no-go property implies that Planck's principle, a form of the second law of the...

To define the work performed on a driven quantum system in a physically sound way has turned out to be a truly non-trivial task, except in some special cases of limited applicability. This topic has been in a focus of intense research recently in the attempts to generalize the classical fluctuation relations into the quantum regime. Here we propose and demonstrate that a calorimetric measurement gives both a theoretical and experimental tool to test the Jarzynski equality (JE...

Information-theoretic approaches provide a promising avenue for extending the laws of thermodynamics to the nanoscale. Here, we provide a general fundamental lower limit, valid for systems with an arbitrary Hamiltonian and in contact with any thermodynamic bath, on the work cost for the implementation of any logical process. This limit is given by a new information measure---the coherent relative entropy---which accounts for the Gibbs weight of each microstate. The coherent r...

We present two applications of emergent local Hamiltonians to speed up quantum adiabatic protocols for isolated noninteracting and weakly interacting fermionic systems in one-dimensional lattices. We demonstrate how to extract maximal work from initial band-insulating states, and how to adiabatically transfer systems from linear and harmonic traps into box traps. Our protocols consist of two stages. The first one involves a free expansion followed by a quench to an emergent l...

The second law of thermodynamics, formulated as an ultimate bound on the maximum extractable work, has been rigorously derived in multiple scenarios. However, the unavoidable limitations that emerge due to the lack of control on small systems are often disregarded when deriving such bounds, which is specifically important in the context of quantum thermodynamics. Here, we study the maximum extractable work with limited control over the working system and its interaction with ...