skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.


Title: Thermodynamics of deterministic finite automata operating locally and periodically
Abstract Real-world computers have operational constraints that cause nonzero entropy production (EP). In particular, almost all real-world computers are ‘periodic’, iteratively undergoing the same physical process; and ‘local’, in that subsystems evolve whilst physically decoupled from the rest of the computer. These constraints are so universal because decomposing a complex computation into small, iterative calculations is what makes computers so powerful. We first derive the nonzero EP caused by the locality and periodicity constraints for deterministic finite automata (DFA), a foundational system of computer science theory. We then relate this minimal EP to the computational characteristics of the DFA. We thus divide the languages recognised by DFA into two classes: those that can be recognised with zero EP, and those that necessarily have non-zero EP. We also demonstrate the thermodynamic advantages of implementing a DFA with a physical process that is agnostic about the inputs that it processes.  more » « less
Award ID(s):
2221345
PAR ID:
10478349
Author(s) / Creator(s):
;
Publisher / Repository:
IOP Publishing
Date Published:
Journal Name:
New Journal of Physics
Volume:
25
Issue:
12
ISSN:
1367-2630
Format(s):
Medium: X Size: Article No. 123013
Size(s):
Article No. 123013
Sponsoring Org:
National Science Foundation
More Like this
  1. Utilizing distributed renewable and energy storage resources via peer-to-peer (P2P) energy trading has long been touted as a solution to improve energy system’s resilience and sustainability. Consumers and prosumers (those who have energy generation resources), however, do not have expertise to engage in repeated P2P trading, and the zero-marginal costs of renewables present challenges in determining fair market prices. To address these issues, we propose a multi-agent reinforcement learning (MARL) framework to help automate consumers’ bidding and management of their solar PV and energy storage resources, under a specific P2P clearing mechanism that utilizes the so-called supply-demand ratio. In addition, we show how the MARL framework can integrate physical network constraints to realize decentralized voltage control, hence ensuring physical feasibility of the P2P energy trading and paving ways for real-world implementations. 
    more » « less
  2. The relationship between the thermodynamic and computational properties of physical systems has been a major theoretical interest since at least the 19th century. It has also become of increasing practical importance over the last half-century as the energetic cost of digital devices has exploded. Importantly, real-world computers obey multiple physical constraints on how they work, which affects their thermodynamic properties. Moreover, many of these constraints apply to both naturally occurring computers, like brains or Eukaryotic cells, and digital systems. Most obviously, all such systems must finish their computation quickly, using as few degrees of freedom as possible. This means that they operate far from thermal equilibrium. Furthermore, many computers, both digital and biological, are modular, hierarchical systems with strong constraints on the connectivity among their subsystems. Yet another example is that to simplify their design, digital computers are required to be periodic processes governed by a global clock. None of these constraints were considered in 20th-century analyses of the thermodynamics of computation. The new field of stochastic thermodynamics provides formal tools for analyzing systems subject to all of these constraints. We argue here that these tools may help us understand at a far deeper level just how the fundamental thermodynamic properties of physical systems are related to the computation they perform. 
    more » « less
  3. Developing a thermodynamic theory of computation is a challenging task at the interface of nonequilibrium thermodynamics and computer science. In particular, this task requires dealing with difficulties such as stochastic halting times, unidirectional (possibly deterministic) transitions, and restricted initial conditions, features common in real-world computers. Here, we present a framework which tackles all such difficulties by extending the martingale theory of nonequilibrium thermodynamics to generic nonstationary Markovian processes, including those with broken detailed balance and/or absolute irreversibility. We derive several universal fluctuation relations and second-law-like inequalities that provide both lower and upper bounds on the intrinsic dissipation (mismatch cost) associated with any periodic process—in particular, the periodic processes underlying all current digital computation. Crucially, these bounds apply even if the process has stochastic stopping times, as it does in many computational machines. We illustrate our results with exhaustive numerical simulations of deterministic finite automata processing bit strings, one of the fundamental models of computation from theoretical computer science. We also provide universal equalities and inequalities for the acceptance probability of words of a given length by a deterministic finite automaton in terms of thermodynamic quantities, and outline connections between computer science and stochastic resetting. Our results, while motivated from the computational context, are applicable far more broadly. 
    more » « less
  4. null (Ed.)
    In many network applications, it may be desirable to conceal certain target nodes from detection by a data collector, who is using a crawling algorithm to explore a network. For example, in a computer network, the network administrator may wish to protect those computers (target nodes) with sensitive information from discovery by a hacker who has exploited vulnerable machines and entered the network. These networks are often protected by hiding the machines (nodes) from external access, and allow only fixed entry points into the system (protection against external attacks). However, in this protection scheme, once one of the entry points is breached, the safety of all internal machines is jeopardized (i.e., the external attack turns into an internal attack). In this paper, we view this problem from the perspective of the data protector. We propose the Node Protection Problem: given a network with known entry points, which edges should be removed/added so as to protect as many target nodes from the data collector as possible? A trivial way to solve this problem would be to simply disconnect either the entry points or the target nodes – but that would make the network non-functional. Accordingly, we impose certain constraints: for each node, only (1 − r) fraction of its edges can be removed, and the resulting network must not be disconnected. We propose two novel scoring mechanisms - the Frequent Path Score and the Shortest Path Score. Using these scores, we propose NetProtect, an algorithm that selects edges to be removed or added so as to best impede the progress of the data collector. We show experimentally that NetProtect outperforms baseline node protection algorithms across several real-world networks. In some datasets, With 1% of the edges removed by NetProtect, we found that the data collector requires up to 6 (4) times the budget compared to the next best baseline in order to discover 5 (50) nodes. 
    more » « less
  5. Abstract Individuals’ socio-demographic and economic characteristics crucially shape the spread of an epidemic by largely determining the exposure level to the virus and the severity of the disease for those who got infected. While the complex interplay between individual characteristics and epidemic dynamics is widely recognised, traditional mathematical models often overlook these factors. In this study, we examine two important aspects of human behaviour relevant to epidemics: contact patterns and vaccination uptake. Using data collected during the COVID-19 pandemic in Hungary, we first identify the dimensions along which individuals exhibit the greatest variation in their contact patterns and vaccination uptake. We find that generally higher socio-economic groups of the population have a higher number of contacts and a higher vaccination uptake with respect to disadvantaged groups. Subsequently, we propose a data-driven epidemiological model that incorporates these behavioural differences. Finally, we apply our model to analyse the fourth wave of COVID-19 in Hungary, providing valuable insights into real-world scenarios. By bridging the gap between individual characteristics and epidemic spread, our research contributes to a more comprehensive understanding of disease dynamics and informs effective public health strategies. 
    more » « less