5,511 research outputs found
Thermodynamics of computing with circuits
Digital computers implement computations using circuits, as do many naturally
occurring systems (e.g., gene regulatory networks). The topology of any such
circuit restricts which variables may be physically coupled during the
operation of a circuit. We investigate how such restrictions on the physical
coupling affects the thermodynamic costs of running the circuit. To do this we
first calculate the minimal additional entropy production that arises when we
run a given gate in a circuit. We then build on this calculation, to analyze
how the thermodynamic costs of implementing a computation with a full circuit,
comprising multiple connected gates, depends on the topology of that circuit.
This analysis provides a rich new set of optimization problems that must be
addressed by any designer of a circuit, if they wish to minimize thermodynamic
costs.Comment: 26 pages (6 of appendices), 5 figure
Complete integrability of information processing by biochemical reactions
Statistical mechanics provides an effective framework to investigate
information processing in biochemical reactions. Within such framework
far-reaching analogies are established among (anti-) cooperative collective
behaviors in chemical kinetics, (anti-)ferromagnetic spin models in statistical
mechanics and operational amplifiers/flip-flops in cybernetics. The underlying
modeling -- based on spin systems -- has been proved to be accurate for a wide
class of systems matching classical (e.g. Michaelis--Menten, Hill, Adair)
scenarios in the infinite-size approximation. However, the current research in
biochemical information processing has been focusing on systems involving a
relatively small number of units, where this approximation is no longer valid.
Here we show that the whole statistical mechanical description of reaction
kinetics can be re-formulated via a mechanical analogy -- based on completely
integrable hydrodynamic-type systems of PDEs -- which provides explicit
finite-size solutions, matching recently investigated phenomena (e.g.
noise-induced cooperativity, stochastic bi-stability, quorum sensing). The
resulting picture, successfully tested against a broad spectrum of data,
constitutes a neat rationale for a numerically effective and theoretically
consistent description of collective behaviors in biochemical reactions.Comment: 24 pages, 10 figures; accepted for publication in Scientific Report
One-loop diagrams in the Random Euclidean Matching Problem
The matching problem is a notorious combinatorial optimization problem that
has attracted for many years the attention of the statistical physics
community. Here we analyze the Euclidean version of the problem, i.e. the
optimal matching problem between points randomly distributed on a
-dimensional Euclidean space, where the cost to minimize depends on the
points' pairwise distances. Using Mayer's cluster expansion we write a formal
expression for the replicated action that is suitable for a saddle point
computation. We give the diagrammatic rules for each term of the expansion, and
we analyze in detail the one-loop diagrams. A characteristic feature of the
theory, when diagrams are perturbatively computed around the mean field part of
the action, is the vanishing of the mass at zero momentum. In the non-Euclidean
case of uncorrelated costs instead, we predict and numerically verify an
anomalous scaling for the sub-sub-leading correction to the asymptotic average
cost.Comment: 17 pages, 7 figure
Energy-Efficient Algorithms
We initiate the systematic study of the energy complexity of algorithms (in
addition to time and space complexity) based on Landauer's Principle in
physics, which gives a lower bound on the amount of energy a system must
dissipate if it destroys information. We propose energy-aware variations of
three standard models of computation: circuit RAM, word RAM, and
transdichotomous RAM. On top of these models, we build familiar high-level
primitives such as control logic, memory allocation, and garbage collection
with zero energy complexity and only constant-factor overheads in space and
time complexity, enabling simple expression of energy-efficient algorithms. We
analyze several classic algorithms in our models and develop low-energy
variations: comparison sort, insertion sort, counting sort, breadth-first
search, Bellman-Ford, Floyd-Warshall, matrix all-pairs shortest paths, AVL
trees, binary heaps, and dynamic arrays. We explore the time/space/energy
trade-off and develop several general techniques for analyzing algorithms and
reducing their energy complexity. These results lay a theoretical foundation
for a new field of semi-reversible computing and provide a new framework for
the investigation of algorithms.Comment: 40 pages, 8 pdf figures, full version of work published in ITCS 201
Resummation for Nonequilibrium Perturbation Theory and Application to Open Quantum Lattices
Lattice models of fermions, bosons, and spins have long served to elucidate
the essential physics of quantum phase transitions in a variety of systems.
Generalizing such models to incorporate driving and dissipation has opened new
vistas to investigate nonequilibrium phenomena and dissipative phase
transitions in interacting many-body systems. We present a framework for the
treatment of such open quantum lattices based on a resummation scheme for the
Lindblad perturbation series. Employing a convenient diagrammatic
representation, we utilize this method to obtain relevant observables for the
open Jaynes-Cummings lattice, a model of special interest for open-system
quantum simulation. We demonstrate that the resummation framework allows us to
reliably predict observables for both finite and infinite Jaynes-Cummings
lattices with different lattice geometries. The resummation of the Lindblad
perturbation series can thus serve as a valuable tool in validating open
quantum simulators, such as circuit-QED lattices, currently being investigated
experimentally.Comment: 15 pages, 9 figure
Programmable interactions with biomimetic DNA linkers at fluid membranes and interfaces
At the heart of the structured architecture and complex dynamics of
biological systems are specific and timely interactions operated by
biomolecules. In many instances, biomolecular agents are spatially confined to
flexible lipid membranes where, among other functions, they control cell
adhesion, motility and tissue formation. Besides being central to several
biological processes, \emph{multivalent interactions} mediated by reactive
linkers confined to deformable substrates underpin the design of
synthetic-biological platforms and advanced biomimetic materials. Here we
review recent advances on the experimental study and theoretical modelling of a
heterogeneous class of biomimetic systems in which synthetic linkers mediate
multivalent interactions between fluid and deformable colloidal units,
including lipid vesicles and emulsion droplets. Linkers are often prepared from
synthetic DNA nanostructures, enabling full programmability of the
thermodynamic and kinetic properties of their mutual interactions. The coupling
of the statistical effects of multivalent interactions with substrate fluidity
and deformability gives rise to a rich emerging phenomenology that, in the
context of self-assembled soft materials, has been shown to produce exotic
phase behaviour, stimuli-responsiveness, and kinetic programmability of the
self-assembly process. Applications to (synthetic) biology will also be
reviewed.Comment: 63 pages, revie
Precision and Sensitivity in Detailed-Balance Reaction Networks
We study two specific measures of quality of chemical reaction networks,
Precision and Sensitivity. The two measures arise in the study of sensory
adaptation, in which the reaction network is viewed as an input-output system.
Given a step change in input, Sensitivity is a measure of the magnitude of the
response, while Precision is a measure of the degree to which the system
returns to its original output for large time. High values of both are
necessary for high-quality adaptation.
We focus on reaction networks without dissipation, which we interpret as
detailed-balance, mass-action networks. We give various upper and lower bounds
on the optimal values of Sensitivity and Precision, characterized in terms of
the stoichiometry, by using a combination of ideas from matroid theory and
differential-equation theory.
Among other results, we show that this class of non-dissipative systems
contains networks with arbitrarily high values of both Sensitivity and
Precision. This good performance does come at a cost, however, since certain
ratios of concentrations need to be large, the network has to be extensive, or
the network should show strongly different time scales
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