Entropy production and time-asymmetry in the presence of strong interactions

It is known that the equilibrium properties of open classical systems that are strongly coupled to a heat bath are described by a set of thermodynamic potentials related to the system's Hamiltonian of mean force. By adapting this framework to a more general class of non-equilibrium states, we show that the equilibrium properties of the bath can be well-defined, even when the system is arbitrarily far from equilibrium and correlated with the bath. These states, which retain a notion of temperature, take the form of conditional equilibrium distributions. For out-of-equilibrium processes we show that the average entropy production quantifies the extent to which the system-bath state is driven away from the conditional equilibrium distribution. In addition, we show that the stochastic entropy production satisfies a generalised Crooks relation and can be used to quantify time-asymmetry of correlated non-equilibrium processes. These results naturally extend the familiar properties of entropy production in weakly-coupled systems to the strong coupling regime. Experimental measurements of the entropy production at strong coupling could be pursued using optomechanics or trapped ion systems, which allow strong coupling to be engineered.Comment: 8 pages, 1 figure, comments welcom

Leggett-Garg inequalities for quantum fluctuating work

The Leggett-Garg inequalities serve to test whether or not quantum correlations in time can be explained within a classical macrorealistic framework. We apply this test to thermodynamics and derive a set of Leggett- Garg inequalities for the statistics of fluctuating work done on a quantum system unitarily driven in time. It is shown that these inequalities can be violated in a driven two-level system, thereby demonstrating that there exists no general macrorealistic description of quantum work. These violations are shown to emerge within the standard Two-Projective-Measurement scheme as well as for alternative definitions of fluctuating work that are based on weak measurement. Our results elucidate the influences of temporal correlations on work extraction in the quantum regime and highlight a key difference between quantum and classical thermodynamics.Comment: v2, 1 figure, accepted version to appear in Entropy (Special Issue on "Quantum Thermodynamics II"

Bounds on Localized Modes in the Crystal Impurity Problem

Using general properties of the crystal site representation normal mode matrix, we provide some very simple bounds on localized modes in simple, body-centered and face-centered cubic crystals with substitutional point defects. We derive a trace condition constraint on the net change in crystal eigenfrequencies caused by the introduction of a defect, with the condition being a completely general one which holds for any combination of central and non-central crystal force-constants and for all-neighbor interactions. Using this condition we show that the sufficient condition for producing localized modes in an arbitrary cubic crystal by a mass change at the defect site is that the defect mass be less than one half of that of the host atom mass which it replaces, and that the sufficient condition for producing localized modes in an arbitrary cubic crystal by force-constant changes alone is that the defect site self force-constant be greater than twice that of the pure crystal self force-constant of the host atom which it replaces.Comment: 25 pages, 3 figures, revtex4. Updated version contains much more general bounds than original versio