Time-reversal symmetric work distributions for closed quantum dynamics in the histories framework

A central topic in the emerging field of quantum thermodynamics is the definition of thermodynamic work in the quantum regime. One widely used solution is to define work for a closed system undergoing non-equilibrium dynamics according to the two-point energy measurement scheme. However, due to the invasive nature of measurement the two-point quantum work probability distribution leads to inconsistencies with two pillars of thermodynamics: it breaks the first law and the time-reversal symmetry expected for closed dynamics. We here introduce the quantum histories framework as a method to characterise the thermodynamic properties of the unmeasured, closed dynamics. Extending the classical phase space trajectories to continuous power operator trajectories allows us to derive an alternative quantum work distribution for closed quantum dynamics that fulfils the first law and is time-reversal symmetric. We find that the work distribution of the unmeasured dynamics leads to deviations from the classical Jarzynski equality and can have negative values highlighting distinctly non-classical features of quantum work.Comment: 18 pages, 2 figures, comments welcom

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

Isomorphisms between pattern classes

Isomorphisms p between pattern classes A and B are considered. It is shown that, if p is not a symmetry of the entire set of permutations, then, to within symmetry, A is a subset of one a small set of pattern classes whose structure, including their enumeration, is determined.Comment: 11 page

Delegation versus Communication in the Organization of Government

When a government creates an agency to gather information relevant to policymaking, it faces two critical organizational questions: whether the agency should be given authority to decide on policy or merely supply advice, and what should the policy goals of the agency be. Existing literature on the first question is unable to address the second, because the question of authority becomes moot if the government can simply replicate its preferences within the agency. In contrast, this paper examines both questions within a model of policymaking under time inconsistency, a setting in which the government has a well-known incentive to create an agency with preferences that differ from its own. Thus, our framework permits a meaningful analysis of delegation versus communication with an endogenously chosen agent. The first main finding of the paper is that the government can do equally well with a strategic choice of agent, from which it solicits advice, instead of delegating authority, as long as the time inconsistency problem is not too severe. The second main finding is that the government may strictly prefer seeking advice to delegating authority if there is prior uncertainty with respect to what is the optimal policy.Political Economy, Delegation, Communication, Organizational Design, Time Inconsistency.

Tunneling between edge states in a quantum spin Hall system

We analyze a quantum spin Hall (QSH) device with a point contact connecting two of its edges. The contact supports a net spin tunneling current that can be probed experimentally via a two-terminal resistance measurement. We find that the low-bias tunneling current and the differential conductance exhibit scaling with voltage and temperature that depend nonlinearly on the strength of the electron-electron interaction.Comment: 4 pages, 3 figures; published versio