arXiv subjects

Nicole Yunger Halpern

Publications and source records attributed to Nicole Yunger Halpern.

59 records · Page 4Linked to original sources

arXiv2016

Number of trials required to estimate a free-energy difference, using fluctuation relations

The difference Delta F between free energies has applications in biology, chemistry, and pharmacology. The value of Delta F can be estimated from experiments or simulations, via fluctuation theorems developed in statistical mechanics. Calculating the error in a Delta F estimate is difficult. Worse, atypical trials dominate estimates. How many trials one should perform was estimated roughly in [Jarzynski, Phys. Rev. E 73, 046105 (2006)]. We enhance the approximation with information-theoretic strategies: We quantify "dominance" with a tolerance parameter chosen by the experimenter or simulator. We bound the number of trials one should expect to perform, using the order-infinity Renyi entropy. The bound can be estimated if one implements the "good practice" of bidirectionality, known to improve estimates of Delta F. Estimating Delta F from this number of trials leads to an error that we bound approximately. Numerical experiments on a weakly interacting dilute classical gas support our analytical calculations.

cond-mat.stat-mech↗

arXiv2016

Beyond heat baths: Generalized resource theories for small-scale thermodynamics

Thermodynamics has recently been extended to small scales with resource theories that model heat exchanges. Real physical systems exchange diverse quantities: heat, particles, angular momentum, etc. We generalize thermodynamic resource theories to exchanges of observables other than heat, to baths other than heat baths, and to free energies other than the Helmholtz free energy. These generalizations are illustrated with "grand-potential" theories that model movements of heat and particles. Free operations include unitaries that conserve energy and particle number. From this conservation law and from resource-theory principles, the grand-canonical form of the free states is derived. States are shown to form a quasiorder characterized by free operations, d-majorization, the hypothesis-testing entropy, and rescaled Lorenz curves. We calculate the work distillable from, and we bound the work cost of creating, a state. These work quantities can differ but converge to the grand potential in the thermodynamic limit. Extending thermodynamic resource theories beyond heat baths, we open diverse realistic systems to modeling with one-shot statistical mechanics. Prospective applications such as electrochemical batteries are hoped to bridge one-shot theory to experiments.

quant-ph↗

arXiv2015

Introducing one-shot work into fluctuation relations

Two approaches to small-scale and quantum thermodynamics are fluctuation relations and one-shot statistical mechanics. Fluctuation relations (such as Crooks' Theorem and Jarzynski's Equality) relate nonequilibrium behaviors to equilibrium quantities such as free energy. One-shot statistical mechanics involves statements about every run of an experiment, not just about averages over trials. We investigate the relation between the two approaches. We show that both approaches feature the same notions of work and the same notions of probability distributions over possible work values. The two approaches are alternative toolkits with which to analyze these distributions. To combine the toolkits, we show how one-shot work quantities can be defined and bounded in contexts governed by Crooks' Theorem. These bounds provide a new bridge from one-shot theory to experiments originally designed for testing fluctuation theorems.

cond-mat.stat-mech↗

arXiv2015

The resource theory of informational nonequilibrium in thermodynamics

We review recent work on the foundations of thermodynamics in the light of quantum information theory. We adopt a resource-theoretic perspective, wherein thermodynamics is formulated as a theory of what agents can achieve under a particular restriction, namely, that the only state preparations and transformations that they can implement for free are those that are thermal at some fixed temperature. States that are out of thermal equilibrium are the resources. We consider the special case of this theory wherein all systems have trivial Hamiltonians (that is, all of their energy levels are degenerate). In this case, the only free operations are those that add noise to the system (or implement a reversible evolution) and the only nonequilibrium states are states of informational nonequilibrium, that is, states that deviate from the maximally mixed state. The degree of this deviation we call the state's nonuniformity; it is the resource of interest here, the fuel that is consumed, for instance, in an erasure operation. We consider the different types of state conversion: exact and approximate, single-shot and asymptotic, catalytic and noncatalytic. In each case, we present the necessary and sufficient conditions for the conversion to be possible for any pair of states, emphasizing a geometrical representation of the conditions in terms of Lorenz curves. We also review the problem of quantifying the nonuniformity of a state, in particular through the use of generalized entropies. Quantum state conversion problems in this resource theory can be shown to be always reducible to their classical counterparts, so that there are no inherently quantum-mechanical features arising in such problems. This body of work also demonstrates that the standard formulation of the second law of thermodynamics is inadequate as a criterion for deciding whether or not a given state transition is possible.

quant-ph↗

arXiv2013

Parity anomaly and Landau-level lasing in strained photonic honeycomb lattices

We describe the formation of highly degenerate, Landau-level-like amplified states in a strained photonic honeycomb lattice in which amplification breaks the sublattice symmetry. As a consequence of the parity anomaly, the zeroth Landau level is localized on a single sublattice and possesses an enhanced or reduced amplification rate. The spectral properties of the higher Landau levels are constrained by a generalized time-reversal symmetry. In the setting of two-dimensional photonic crystal lasers, the anomaly directly affects the mode selection and lasing threshold while in three-dimensional photonic lattices it can be probed via beam dynamics.

cond-mat.mes-hall↗