arXiv subjects

David H. Wolpert

Publications and source records attributed to David H. Wolpert.

At least 19 recordsLinked to original sources

arXiv2026

Strengthened second law for periodic processes

Many physical systems evolve under periodic driving: the same control protocol is applied again and again, even though the state of the system itself need not return to where it started after each cycle. We derive a physics-independent lower bound on the entropy production of \emph{any} periodic process modeled by the evolution of an initial distribution $p_0$ by a repeated application of the same map $G$. This is a strict strengthening of the second law of thermodynamics for periodic processes. It does not require that the single-period dynamics arise from a CTMC, satisfy (local) detailed balance, or be subject to other typical restrictions. We discuss its application to spins in the Curie-Weiss model and Deterministic Finite Automata, with possible extensions to other uniform computers.

cond-mat.stat-mech↗

arXiv2026

Finite relaxation protocols with minimal dissipation

Work extraction from nonequilibrium systems is a major challenge across biological, chemical, physical, and engineering systems. Idealized protocols generally require a quasistatic relaxation stage in which the Hamiltonian is gradually adjusted through a continuum of intermediaries. Here, we consider protocols restricted to a finite number $N$ of intermediary Hamiltonians, consisting of a sequence of quench-relax steps. We determine the sequence of quenches that minimizes the dissipated work, which can be expressed in terms of a recurrence involving the Lambert function. The optimal sequence converges to the Fisher-Rao geodesic, saturating known leading-order dissipation bounds at large $N$. We obtain lower bounds on work extraction from a nonequilibrium distribution as a function of its Fisher-Rao distance to equilibrium. We extend and apply the framework in two simple models: (i) an optical trap experiment, showing that the optimal intermediary distribution can be bimodal even for unimodal initial and final distributions, and (ii) an enzyme-catalyzed reaction, showing that that accounting for relaxation time in addition to dissipation can favor barrier-lowering.

cond-mat.stat-mech↗

arXiv2026

Computational foundations of the human world

Human societies continuously transform scattered information into collective judgments and coordinated action, whether through markets discovering prices, governments allocating resources, communities enforcing norms, or science converging on reliable claims. Importantly, the computational difficulty of collective decision-making, particularly the time and communication required to reach solutions, imposes fundamental constraints on social organization. While theoretical computer science offers formal tools for analyzing such problems, for instance, by analyzing resource requirements, including time and memory, surprisingly, there is no domain of social science that focuses on the nature of computation in the human world. This perspective argues that we now have the opportunity to deploy these computational frameworks to study human social organization, opening research directions at the intersection of computer science and social science. We highlight core social phenomena that can be framed as computational, including (i) distributed consensus and coordinated action, (ii) societal restructuring with scale, (iii) hierarchical and modular structure, and (iv) externalized memory systems. We identify several concepts from theoretical computer science that may provide insight into these phenomena, especially emphasizing more recently developed approaches beyond the paradigm of Turing~Machines and worst-case computational complexity.

cs.SI↗

arXiv2026

Implications of computer science theory for the simulation hypothesis

The simulation hypothesis has recently excited renewed interest in the physics and philosophy communities. However, the hypothesis specifically concerns {\textit{computers}} that simulate physical universes. So to formally investigate the hypothesis, we need to understand it in terms of computer science (CS) theory. In addition we need a formal way to couple CS theory with physics. Here I couple those fields by using the physical Church-Turing thesis. This allow me to exploit Kleene's second recursion, to prove that not only is it possible for {us} to be a simulation being run on a computer, but that we might be in a simulation being run a computer \emph{by us}. In such a ``self-simulation'', there would be two identical instances of us, both equally ``real''. I then use Rice's theorem to derive impossibility results concerning simulation and self-simulation; derive implications for (self-)simulation if we are being simulated in a program using fully homomorphic encryption; and briefly investigate the graphical structure of universes simulating other universes which contain computers running their own simulations. I end by describing some of the possible avenues for future research. While motivated in terms of the simulation hypothesis, the results in this paper are direct consequences of the Church-Turing thesis. So they apply far more broadly than the simulation hypothesis.

cs.LO↗

arXiv2025

What does it mean for a system to compute?

Many real-world dynamic systems, both natural and artificial, are understood to be performing computations. For artificial dynamic systems, explicitly designed to perform computation - such as digital computers - by construction, we can identify which aspects of the dynamic system match the input and output of the computation that it performs, as well as the aspects of the dynamic system that match the intermediate logical variables of that computation. In contrast, in many naturally occurring dynamical systems that we understand to be computers, even though we neither designed nor constructed them - such as the human brain - it is not a priori clear how to identify the computation we presume to be encoded in the dynamic system. Regardless of their origin, dynamical systems capable of computation can, in principle, be mapped onto corresponding abstract computational machines that perform the same operations. In this paper, we begin by surveying a wide range of dynamic systems whose computational properties have been studied. We then introduce a very broadly applicable framework for identifying what computations(s) are emulated by a given dynamic system. After an introduction, we summarize key examples of dynamical systems whose computational properties have been studied. We then introduce a very broadly applicable framework that defines the computation performed by a given dynamical system in terms of maps between that system's evolution and the evolution of an abstract computational machine. We illustrate this framework with several examples from the literature, in particular discussing why some of those examples do not fully fall within the remit of our framework. We also briefly discuss several related issues, such as uncomputability in dynamical systems, and how to quantify the value of computation in naturally occurring computers.

physics.comp-ph↗

arXiv2025

Uncertainty relations and fluctuation theorems for Bayes nets

Recent research has considered the stochastic thermodynamics of multiple interacting systems, representing the overall system as a Bayes net. I derive fluctuation theorems governing the entropy production (EP)of arbitrary sets of the systems in such a Bayes net. I also derive ``conditional'' fluctuation theorems, governing the distribution of EP in one set of systems conditioned on the EP of a different set of systems. I then derive thermodynamic uncertainty relations relating the EP of the overall system to the precisions of probability currents within the individual systems.

cond-mat.stat-mech↗

arXiv2025

Stochastic thermodynamics of computation

One of the major resource requirements of computers - ranging from biological cells to human brains to high-performance (engineered) computers - is the energy used to run them. Those costs of performing a computation have long been a focus of research in physics, going back to the early work of Landauer. One of the most prominent aspects of computers is that they are inherently nonequilibrium systems. However, the early research was done when nonequilibrium statistical physics was in its infancy, which meant the work was formulated in terms of equilibrium statistical physics. Since then there have been major breakthroughs in nonequilibrium statistical physics, which are allowing us to investigate the myriad aspects of the relationship between statistical physics and computation, extending well beyond the issue of how much work is required to erase a bit. In this paper I review some of this recent work on the `stochastic thermodynamics of computation'. After reviewing the salient parts of information theory, computer science theory, and stochastic thermodynamics, I summarize what has been learned about the entropic costs of performing a broad range of computations, extending from bit erasure to loop-free circuits to logically reversible circuits to information ratchets to Turing machines. These results reveal new, challenging engineering problems for how to design computers to have minimal thermodynamic costs. They also allow us to start to combine computer science theory and stochastic thermodynamics at a foundational level, thereby expanding both.

cond-mat.stat-mech↗

arXiv2025

Measuring amount of computation done by C.elegans using whole brain neural activity

Many dynamical systems found in biology, ranging from genetic circuits to the human brain to human social systems, are inherently computational. Although extensive research has explored their resulting functions and behaviors, the underlying computations often remain elusive. Even the fundamental task of quantifying the \textit{amount} of computation performed by a dynamical system remains under-investigated. In this study we address this challenge by introducing a novel framework to estimate the amount of computation implemented by an arbitrary physical system based on empirical time-series of its dynamics. This framework works by forming a statistical reconstruction of that dynamics, and then defining the amount of computation in terms of both the complexity and fidelity of this reconstruction. We validate our framework by showing that it appropriately distinguishes the relative amount of computation across different regimes of Lorenz dynamics and various computation classes of cellular automata. We then apply this framework to neural activity in \textit{Caenorhabditis elegans}, as captured by calcium imaging. By analyzing time-series neural data obtained from the fluorescent intensity of the calcium indicator GCaMP, we find that high and low amounts of computation are required, respectively, in the neural dynamics of freely moving and immobile worms. Our analysis further sheds light on the amount of computation performed when the system is in various locomotion states. In sum, our study refines the definition of computational amount from time-series data and highlights neural computation in a simple organism across distinct behavioral states.

q-bio.NC↗

arXiv2025

The computational power of a human society: a new model of social evolution

Social evolutionary theory seeks to explain increases in the scale and complexity of human societies, from origins to present. Over the course of the twentieth century, social evolutionary theory largely fell out of favor as a way of investigating human history, just when advances in complex systems science and computer science saw the emergence of powerful new conceptions of complex systems, and in particular new methods of measuring complexity. We propose that these advances in our understanding of complex systems and computer science should be brought to bear on our investigations into human history. To that end, we present a new framework for modeling how human societies co-evolve with their biotic environments, recognizing that both a society and its environment are computers. This leads us to model the dynamics of each of those two systems using the same, new kind of computational machine, which we define here. For simplicity, we construe a society as a set of interacting occupations and technologies. Similarly, under such a model, a biotic environment is a set of interacting distinct ecological and environmental processes. This provides novel ways to characterize social complexity, which we hope will cast new light on the archaeological and historical records. Our framework also provides a natural way to formalize both the energetic (thermodynamic) costs required by a society as it runs, and the ways it can extract thermodynamic resources from the environment in order to pay for those costs -- and perhaps to grow with any left-over resources.

cs.MA↗

arXiv2024

What can we know about that which we cannot even imagine?

In this essay I will consider a sequence of questions. The first questions concern the biological function of intelligence in general, and cognitive prostheses of human intelligence in particular. These will lead into questions concerning human language, perhaps the most important cognitive prosthesis humanity has ever developed. While it is traditional to rhapsodize about the cognitive power encapsulated in human language, I will emphasize how horribly limited human language is - and therefore how limited our cognitive abilities are, despite their being augmented with language. This will lead to questions of whether human mathematics, being ultimately formulated in terms of human language, is also deeply limited. I will then combine these questions to pose a partial, sort-of, sideways answer to the guiding concern of this essay: what we can ever discern about that we cannot even conceive?

physics.hist-ph↗

arXiv2024

Strengthened second law for multi-dimensional systems coupled to multiple thermodynamic reservoirs

The second law of thermodynamics can be formulated as a restriction on the evolution of the entropy of any system undergoing Markovian dynamics. Here I show that this form of the second law is strengthened for multi-dimensional, complex systems, coupled to multiple thermodynamic reservoirs, if we have a set of \textit{a priori} constraints restricting how the dynamics of each coordinate can depend on the other coordinates. As an example, this strengthened second law (SSL) applies to complex systems composed of multiple physically separated, co-evolving subsystems, each identified as a coordinate of the overall system. In this example, the constraints concern how the dynamics of some subsystems are allowed to depend on the states of the other subsystems. Importantly the SSL applies to such complex systems even if some of its subsystems can change state simultaneously, which is prohibited in a multipartite process. The SSL also strengthens previously derived bounds on how much work can be extracted from a system using feedback control, if the system is multi-dimensional. Importantly, the SSL does not require local detailed balance. So it potentially applies to complex systems ranging from interacting economic agents to co-evolving biological species.

cond-mat.stat-mech↗

arXiv2024

Entropy production in communication channels

In many complex systems, whether biological or artificial, the thermodynamic costs of communication among their components are large. These systems also tend to split information transmitted between any two components across multiple channels. A common hypothesis is that such inverse multiplexing strategies reduce total thermodynamic costs. So far, however, there have been no physics-based results supporting this hypothesis. This gap existed partially because we have lacked a theoretical framework that addresses the interplay of thermodynamics and information in off-equilibrium systems. Here we present the first study that rigorously combines such a framework, stochastic thermodynamics, with Shannon information theory. We develop a minimal model that captures the fundamental features common to a wide variety of communication systems, and study the relationship between the entropy production of the communication process and the channel capacity, the canonical measure of the communication capability of a channel. In contrast to what is assumed in previous works not based on first principles, we show that the entropy production is not always a convex and monotonically increasing function of the channel capacity. However, those two properties are recovered for sufficiently high channel capacity. These results clarify when and how to split a single communication stream across multiple channels.

cond-mat.stat-mech↗

arXiv2024

Game Mining: How to Make Money from those about to Play a Game

It is known that a player in a noncooperative game can benefit by publicly restricting his possible moves before play begins. We show that, more generally, a player may benefit by publicly committing to pay an external party an amount that is contingent on the game's outcome. We explore what happens when external parties -- who we call ``game miners'' -- discover this fact and seek to profit from it by entering an outcome-contingent contract with the players. We analyze various structured bargaining games between miners and players for determining such an outcome-contingent contract. These bargaining games include playing the players against one another, as well as allowing the players to pay the miner(s) for exclusivity and first-mover advantage. We establish restrictions on the strategic settings in which a game miner can profit and bounds on the game miner's profit. We also find that game miners can lead to both efficient and inefficient equilibria.

econ.GN↗

arXiv2023

Memory Systems, the Epistemic Arrow of Time, and the Second Law

The epistemic arrow of time is the fact that our knowledge of the past seems to be both of a different kind and more detailed than our knowledge of the future. Just like with the other arrows of time, it has often been speculated that the epistemic arrow arises due to the second law of thermodynamics. In this paper we investigate the epistemic arrow of time, using a fully formal framework. We begin by defining a memory system as any physical system whose present state can provide information about the state of the external world at some time other than the present. We then identify two types of memory systems in our universe, along with an important special case of the first type, which we distinguish as a third type of memory system. We show that two of these types of memory system are time-symmetric, able to provide knowledge about both the past and the future. However, the third type of memory systems exploits the second law of thermodynamics in all of its instances we find in our universe. The result is that in our universe, this type of memory system only ever provides information about the past. Finally, we argue that human memory is of this third type, completing the argument. Our analysis is indebted to prior work in Wolpert 1992, but expands and improves upon this work in several respects.

physics.hist-ph↗

arXiv2023

Thermodynamics of deterministic finite automata operating locally and periodically

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.

cond-mat.stat-mech↗

arXiv2023

Stochastic thermodynamics of multiple co-evolving systems -- beyond multipartite processes

Many dynamical systems consist of multiple, co-evolving subsystems (degrees of freedom). These subsystems often depend upon each other in a way that restricts the overall system's dynamics. How does this network of dependencies affect the system's thermodynamics? Prior studies in the stochastic thermodynamics of multipartite processes (MPPs) have approached this question by restricting the system to allow only one subsystem to change state at a time. However, in many real systems, such as chemical reaction networks or electronic circuits, multiple subsystems must change state together. Therefore, studies of MPPs do not apply to such systems. Here, we investigate the thermodynamics of composite processes, in which subsets of subsystems are allowed to change state simultaneously. These subsets correspond to the subsystems that interact with a single mechanism (e.g., a thermal or chemical reservoir) that is coupled to the system. An MPP is simply a (subcase of a) composite process in which all such subsets have cardinality one. We demonstrate the power of the composite systems framework to study the thermodynamics of multiple, co-evolving subsystems. In particular, we derive thermodynamic uncertainty relations for information flows in composite processes. We also derive strengthened speed limits for composite processes. Our results apply to a much broader class of dynamical systems than do results for MPPs, and could guide future studies of the thermodynamics of distributed computational systems.

cond-mat.stat-mech↗

arXiv2023

Nonequilibrium thermodynamics of uncertain stochastic processes

Stochastic thermodynamics is formulated under the assumption of perfect knowledge of all thermodynamic parameters. However, in any real-world experiment, there is non-zero uncertainty about the precise value of temperatures, chemical potentials, energy spectrum, etc. Here we investigate how this uncertainty modifies the theorems of stochastic thermodynamics. We consider two scenarios: in the (called \emph{effective}) scenario we fix the (unknown, randomly generated) experimental apparatus and then repeatedly observe (stochastic) trajectories of the system for that fixed apparatus. In contrast, in a (called \emph{phenomenological}) scenario the (unknown) apparatus is re-generated for each trajectory. We derive expressions for thermodynamic quantities in both scenarios. We also discuss the physical interpretation of effective (scenario) entropy production (EP), derive the effective mismatch cost, and provide a numerical analysis of the effective thermodynamics of a quantum dot implementing bit erasure with uncertain temperature. We then analyze the protocol for moving between two state distributions that maximize effective work extraction. Next, we investigate the effective thermodynamic value of information, focusing on the case where there is a delay between the initialization of the system and the start of the protocol. Finally, we derive the detailed and integrated fluctuation theorems (FTs) for the phenomenological EP. In particular, we show how the phenomenological FTs account for the fact that the longer a trajectory runs, the more information it provides concerning the precise experimental apparatus, and therefore the less EP it generates.

cond-mat.stat-mech↗

arXiv2023

Stochastic Mathematical Systems

We introduce a framework that can be used to model both mathematics and human reasoning about mathematics. This framework involves {stochastic mathematical systems} (SMSs), which are stochastic processes that generate pairs of questions and associated answers (with no explicit referents). We use the SMS framework to define normative conditions for mathematical reasoning, by defining a ``calibration'' relation between a pair of SMSs. The first SMS is the human reasoner, and the second is an ``oracle'' SMS that can be interpreted as deciding whether the question-answer pairs of the reasoner SMS are valid. To ground thinking, we understand the answers to questions given by this oracle to be the answers that would be given by an SMS representing the entire mathematical community in the infinite long run of the process of asking and answering questions. We then introduce a slight extension of SMSs to allow us to model both the physical universe and human reasoning about the physical universe. We then define a slightly different calibration relation appropriate for the case of scientific reasoning. In this case the first SMS represents a human scientist predicting the outcome of future experiments, while the second SMS represents the physical universe in which the scientist is embedded, with the question-answer pairs of that SMS being specifications of the experiments that will occur and the outcome of those experiments, respectively. Next we derive conditions justifying two important patterns of inference in both mathematical and scientific reasoning: i) the practice of increasing one's degree of belief in a claim as one observes increasingly many lines of evidence for that claim, and ii) abduction, the practice of inferring a claim's probability of being correct from its explanatory power with respect to some other claim that is already taken to hold for independent reasons.

math.LO↗