Fluctuations in Single-Shot ϵ\epsilon-Deterministic Work Extraction

There has been an increasing interest in the quantification of nearly deterministic work extraction from a finite number of copies of microscopic particles in finite time. This paradigm, so called single-shot epsilon-deterministic work extraction, considers processes with small failure probabilities. However, the resulting fluctuations in the extracted work entailed by this failure probability have not been studied before. In the standard thermodynamics paradigm fluctuation theorems are powerful tools to study fluctuating quantities. Given that standard fluctuation theorems are inadequate for a single-shot scenario, here we formulate and prove a fluctuation relation specific to the single-shot epsilon-deterministic work extraction to bridge this gap. Our results are general in the sense that we allow the system to be in contact with the heat bath at all times. As a corollary of our theorem we derive the known bounds on the epsilon-deterministic work

Infinite Correlation in Measured Quantum Processes

We show that quantum dynamical systems can exhibit infinite correlations in their behavior when repeatedly measured. We model quantum processes using quantum finite-state generators and take the stochastic language they generate as a representation of their behavior. We analyze two spin-1 quantum systems that differ only in how they are observed. The corresponding language generated has short-range correlation in one case and infinite correlation in the other.Comment: 2 pages, 2 figure

Computation in Finitary Stochastic and Quantum Processes

We introduce stochastic and quantum finite-state transducers as computation-theoretic models of classical stochastic and quantum finitary processes. Formal process languages, representing the distribution over a process's behaviors, are recognized and generated by suitable specializations. We characterize and compare deterministic and nondeterministic versions, summarizing their relative computational power in a hierarchy of finitary process languages. Quantum finite-state transducers and generators are a first step toward a computation-theoretic analysis of individual, repeatedly measured quantum dynamical systems. They are explored via several physical systems, including an iterated beam splitter, an atom in a magnetic field, and atoms in an ion trap--a special case of which implements the Deutsch quantum algorithm. We show that these systems' behaviors, and so their information processing capacity, depends sensitively on the measurement protocol.Comment: 25 pages, 16 figures, 1 table; http://cse.ucdavis.edu/~cmg; numerous corrections and update

Negative Conditional Entropy of Post-Selected States

We define a quantum entropy conditioned on post-selection which has the von Neumann entropy of pure states as a special case. This conditional entropy can take negative values which is consistent with part of a quantum system containing less information than the whole which can be in a pure state. The definition is based on generalised density operators for postselected ensembles. The corresponding density operators are consistent with the quantum generalisation of classical conditional probabilities following Dirac s formalism of quasiprobability distributions

Improving mean-field network percolation models with neighbourhood information and their limitations on highly modular, highly dispersed networks

Mean field theory models of percolation on networks provide analytical predictions of how networks behave under node or edge removal, but these models are not always accurate. Here, we evaluate how well existing models predict network robustness and provide a new model that includes information about the tree-likeness of each node's local neighbourhood. Testing predictions using real-world network data, we show that our new model significantly outperforms others in prediction accuracy for random node and edge removal. We provide evidence that all discussed models are poor in predicting networks with highly modular structure with dispersed modules, identifying this as a general limitation of mean-field percolation models.Comment: 13 pages, 8 figures. Supplementary Materials: 10 pages, 1 table, 5 figure

The thermodynamical cost of some interpretations of quantum theory. Reply to Prunkl and Timpson, and Davidsson

Here we clarify the assumptions made and conclusions reached in our paper "The thermodynamical cost of some interpretations of quantum theory" [Phys. Rev. A 94, 052127 (2016)], at the light of the criticisms of Prunkl and Timpson [Stud. Hist. Philos. Sci. Part B 63, 114 (2018)], and Davidsson (Master thesis, Stockholm University, 2018). We point out some misunderstandings and some weaknesses of the counterexample Prunkl and Timpson present to challenge our conclusion. We thus conclude, once more, that interpretations of quantum theory which consider the probabilities of measurement outcomes to be determined by objective properties of the measured system and satisfy the assumption that the measured system only has finite memory have a thermodynamical cost.Comment: 5 page

Evaluating The Impact Of Species Specialisation On Ecological Network Robustness Using Analytic Methods

Ecological networks describe the interactions between different species, informing us of how they rely on one another for food, pollination and survival. If a species in an ecosystem is under threat of extinction, it can affect other species in the system and possibly result in their secondary extinction as well. Understanding how (primary) extinctions cause secondary extinctions on ecological networks has been considered previously using computational methods. However, these methods do not provide an explanation for the properties which make ecological networks robust, and can be computationally expensive. We develop a new analytic model for predicting secondary extinctions which requires no non-deterministic computational simulation. Our model can predict secondary extinctions when primary extinctions occur at random or due to some targeting based on the number of links per species or risk of extinction, and can be applied to an ecological network of any number of layers. Using our model, we consider how false positives and negatives in network data affect predictions for network robustness. We have also extended the model to predict scenarios in which secondary extinctions occur once species lose a certain percentage of interaction strength, and to model the loss of interactions as opposed to just species extinction. From our model, it is possible to derive new analytic results such as how ecological networks are most robust when secondary species degree variance is minimised. Additionally, we show that both specialisation and generalisation in distribution of interaction strength can be advantageous for network robustness, depending upon the extinction scenario being considered.Comment: 22 pages, 12 figures, 2 table