Qubit thermodynamics far from equilibrium: Two perspectives about the nature of heat and work in the quantum regime.

Considering an entropy-based division of energy transferred into heat and work, we develop an alternative theoretical framework for the thermodynamic analysis of two-level systems. When comparing these results with those obtained using the standard definitions of these quantities, we observe the appearance of a different term of work, which represents the energy cost of rotating the Bloch vector in the presence of the external field that defines the local Hamiltonian. Additionally, we obtain explicit expressions for the temperature, the heat capacity, and the internal entropy production of the system in both paradigms. In order to illustrate our findings we study, from both perspectives, matter-radiation interaction processes for two different systems.

Interspecies evolutionary dynamics mediated by public goods in bacterial quorum sensing.

Bacterial quorum sensing is the communication that takes place between bacteria as they secrete certain molecules into the intercellular medium that later get absorbed by the secreting cells themselves and by others. Depending on cell density, this uptake has the potential to alter gene expression and thereby affect global properties of the community. We consider the case of multiple bacterial species coexisting, referring to each one of them as a genotype and adopting the usual denomination of the molecules they collectively secrete as public goods. A crucial problem in this setting is characterizing the coevolution of genotypes as some of them secrete public goods (and pay the associated metabolic costs) while others do not but may nevertheless benefit from the available public goods. We introduce a network model to describe genotype interaction and evolution when genotype fitness depends on the production and uptake of public goods. The model comprises a random graph to summarize the possible evolutionary pathways the genotypes may take as they interact genetically with one another, and a system of coupled differential equations to characterize the behavior of genotype abundance in time. We study some simple variations of the model analytically and more complex variations computationally. Our results point to a simple trade-off affecting the long-term survival of those genotypes that do produce public goods. This trade-off involves, on the producer side, the impact of producing and that of absorbing the public good. On the nonproducer side, it involves the impact of absorbing the public good as well, now compounded by the molecular compatibility between the producer and the nonproducer. Depending on how these factors turn out, producers may or may not survive.

Out-of-equilibrium quantum thermodynamics in the Bloch sphere: Temperature and internal entropy production.

An explicit expression for the temperature of an open two-level quantum system is obtained as a function of local properties under the hypothesis of weak interaction with the environment. This temperature is defined for both equilibrium and out-of-equilibrium states and coincides with the environment temperature if the system reaches thermal equilibrium with a heat reservoir. Additionally, we show that within this theoretical framework the total entropy production can be partitioned into two contributions: one due to heat transfer and another, associated to internal irreversibilities, related to the loss of internal coherence by the qubit. The positiveness of the heat capacity is established, as well as its consistency with the well-known results at thermal equilibrium. We apply these concepts to two different systems and show that they behave in analogous ways as their classical counterparts.

Quasispecies dynamics with network constraints.

A quasispecies is a set of interrelated genotypes that have reached a stationary state while evolving according to the usual Darwinian principles of selection and mutation. Quasispecies studies invariably assume that it is possible for any genotype to mutate into any other, but recent finds indicate that this assumption is not necessarily true. Here we revisit the traditional quasispecies theory by adopting a network structure to constrain the occurrence of mutations. Such structure is governed by a random-graph model, whose single parameter (a probability p) controls both the graph's density and the dynamics of mutation. We contribute two further modifications to the theory, one to account for the fact that different loci in a genotype may be differently susceptible to the occurrence of mutations, the other to allow for a more plausible description of the transition from adaptation to degeneracy of the quasispecies as p is increased. We give analytical and simulation results for the usual case of binary genotypes, assuming the fitness landscape in which a genotype's fitness decays exponentially with its Hamming distance to the wild type. These results support the theory's assertions regarding the adaptation of the quasispecies to the fitness landscape and also its possible demise as a function of p.

Modeling weight loss and chlorogenic acids content in coffee during roasting.

Roasting is a key step in the production of a high-quality coffee. Roasting degree is directly related to coffee chemical composition and may be determined objectively by weight loss after roasting. Chlorogenic acids (CGA) are thermally labile phenolic compounds that play an important role in the final cup quality and health benefits of coffee. Considering the interest in finding a reliable method to predict weight loss and CGA content in coffee, models have been developed to estimate these parameters during roasting. Weight loss was successfully modeled (r = 0.99) independent of the instant temperature. CGA degradation followed first-order Arrhenius-compliant kinetic models with good predictability (r = 0.98), especially for light to moderately dark samples. In both cases distinct models for Coffea arabica and Coffea canephora were calculated, because of differences in chemical composition and cell wall structure between these species. The proposed models may become important predictive tools in the coffee industry.

Early appraisal of the fixation probability in directed networks.

In evolutionary dynamics, the probability that a mutation spreads through the whole population, having arisen from a single individual, is known as the fixation probability. In general, it is not possible to find the fixation probability analytically given the mutant's fitness and the topological constraints that govern the spread of the mutation, so one resorts to simulations instead. Depending on the topology in use, a great number of evolutionary steps may be needed in each of the simulation events, particularly in those that end with the population containing mutants only. We introduce two techniques to accelerate the determination of the fixation probability. The first one skips all evolutionary steps in which the number of mutants does not change and thereby reduces the number of steps per simulation event considerably. This technique is computationally advantageous for some of the so-called layered networks. The second technique, which is not restricted to layered networks, consists of aborting any simulation event in which the number of mutants has grown beyond a certain threshold value and counting that event as having led to a total spread of the mutation. For advantageous mutations in large populations and regardless of the network's topology, we demonstrate, both analytically and by means of simulations, that using a threshold of about [N/(r-1)](1/4) mutants, where N is the number of simulation events and r is the ratio of the mutants' fitness to that of the remainder of the population, leads to an estimate of the fixation probability that deviates in no significant way from that obtained from the full-fledged simulations. We have observed speedups of two orders of magnitude for layered networks with 10,000 nodes.

Network growth for enhanced natural selection.

Natural selection and random drift are competing phenomena for explaining the evolution of populations. Combining a highly fit mutant with a population structure that improves the odds that the mutation spreads through the whole population tips the balance in favor of natural selection. The probability that the spread occurs, known as the fixation probability, depends heavily on how the population is structured. Certain topologies, albeit highly artificially contrived, have been shown to exist that favor fixation. We present a randomized mechanism for network growth that is loosely inspired in some of these topologies' key properties and demonstrate, through simulations, that it is capable of giving rise to structured populations for which the fixation probability significantly surpasses that of an unstructured population. This discovery provides important support to the notion that natural selection can be enhanced over random drift in naturally occurring population structures.

Generalized memory associativity in a network model for the neuroses.

We review concepts introduced in earlier work, where a neural network mechanism describes some mental processes in neurotic pathology and psychoanalytic working-through, as associative memory functioning, according to the findings of Freud. We developed a complex network model, where modules corresponding to sensorial and symbolic memories interact, representing unconscious and conscious mental processes. The model illustrates Freud's idea that consciousness is related to symbolic and linguistic memory activity in the brain. We have introduced a generalization of the Boltzmann machine to model memory associativity. Model behavior is illustrated with simulations and some of its properties are analyzed with methods from statistical mechanics.

Emergence of scale-free networks from local connectivity and communication trade-offs.

We suggest a mechanism of connectivity evolution in networks to account for the emergence of scale-free behavior. The mechanism works on a fixed set of nodes and promotes growth from a minimally connected initial topology by the addition of edges. A new edge is added between two nodes depending on the trade-off between a gain and a cost function of local connectivity and communication properties. We report on simulation results that indicate the appearance of power-law distributions of node degrees for selected parameter combinations.