From Quantum Dynamics to the Second Law of Thermodynamics

We treat a quantum mechanical system with certain general properties which are expected to be common in macroscopic quantum systems. Starting from a PURE initial state (which may not describe an equilibrium) in which energy is mildly concentrated at a single value, we consider a time evolution determined by a time-dependent Hamiltonian as a model of an adiabatic operation in thermodynamics. We take a family of operations with the same procedure and various ``waiting times.'' ...

Based on quantum statistical mechanics and microscopic quantum dynamics, we prove Planck's and Kelvin's principles for macroscopic systems in a general and realistic setting. We consider a hybrid quantum system that consists of the thermodynamic system, which is initially in thermal equilibrium, and the "apparatus" which operates on the former, and assume that the whole system evolves autonomously. This provides a satisfactory derivation of the second law for macroscopic syst...

It has been recently claimed that no protocol for measuring quantum work can satisfy standard required physical principles, casting doubts on the compatibility between quantum mechanics, thermodynamics, and the classical limit. In this Letter, we present a solution for this incompatibility. We demonstrate that the standard formulation of these principles fails to address the classical limit properly. By proposing changes in this direction, we prove that all the essential prin...

Quantum dynamics controlled by a time-dependent coupling constant are studied. It is proven that an energy eigenstate expectation value of work done by the system in a quench process cannot exceed the work in the corresponding quasi-static process, if and only if the energy eigenvalue is a concave function of the coupling constant. We propose this concavity of energy eigenvalues as a new universal criterion for quantum dynamical systems to satisfy the second law of thermodyna...

With a class of quantum heat engines which consists of two-energy-eigenstate systems undergoing, respectively, quantum adiabatic processes and energy exchanges with heat baths at different stages of a cycle, we are able to clarify some important aspects of the second law of thermodynamics. The quantum heat engines also offer a practical way, as an alternative to Szilard's engine, to physically realise Maxwell's daemon. While respecting the second law on the average, they are ...

Underlying the classical thermodynamic principles are analogous microscopic laws, arising from the fundamental axioms of quantum mechanics. These define quantum thermodynamic variables such as quantum work and heat and characterize the possible transformations of open quantum systems. The foremost quantum thermodynamic law is a simple statement concerning the conservation of energy. Nevertheless, there exist ambiguity and disagreement regarding the precise partition of a quan...

This work presents a general unifying theoretical framework for quantum non-equilibrium systems. It is based on a re-statement of the dynamical problem as one of inferring the distribution of collision events that move a system toward thermal equilibrium from an arbitrary starting distribution. Using a form based on maximum entropy for this transition distribution leads to a statistical description of open quantum systems with strong parallels to the conventional, maximum-ent...

A short introduction on quantum thermodynamics is given and three new topics are discussed: 1) Maximal work extraction from a finite quantum system. The thermodynamic prediction fails and a new, general result is derived, the ``ergotropy''. 2) In work extraction from two-temperature setups, the presence of correlations can push the effective efficiency beyond the Carnot bound. 3) In the presence of level crossing, non-slow changes may be more optimal than slow ones.

The Kullback-Leibler inequality is a way of comparing any two density matrices. A technique to set up the density matrix for a physical system is to use the maximum entropy principle, given the entropy as a functional of the density matrix, subject to known constraints. In conjunction with the master equation for the density matrix, these two ingredients allow us to formulate the second law of thermodynamics in its widest possible setting. Thus problems arising in both quantu...

Quantum thermodynamics aims to explore quantum features to enhance energy conversion beyond classical limits. While significant progress has been made, the understanding of caloric potentials in quantum systems remains incomplete. In this context, this study focuses on deriving general expressions for these caloric potentials by developing a quantum Maxwell relationship obtained from a thermal average form of the Ehrenfest theorem. Our results recover the classical cases and ...