Search

This article details a correction to: Wolpert, D.H., Price, M.H., Crabtree, S.A., Kohler, T.A., Jost, J., Evans, J., Stadler, P.F., Shimao, H. and Laubichler, M.D. (2024) ‘The Past as a Stochastic Process’, Journal of Computer Applications in Archaeology, 7(1), p. 134–152. Available at: https://doi.org/10.5334/jcaa.113.

Historical processes manifest remarkable diversity. Nevertheless, scholars have long attempted, with some success, to identify patterns and categorize historical actors and influences. A stochastic process framework provides a structured approach for the analysis of large historical datasets that allows for detection of sometimes surprising patterns, identification of relevant causal actors both endogenous and exogenous to the process, and comparison between different historical cases. The combination of data, analytical tools and the organizing theoretical framework of stochastic processes complements traditional narrative approaches in history and archaeology.

Abstract The first synthesis of organic Tri 6 Di 9 cages is presented. Two structurally distinct Tri 6 Di 9 cages were synthesised by combining a highly fluorinated aldehyde with two ditopic amines. Although the pure compounds could not be isolated despite many attempts, the information obtained is critical for the future design of large supramolecular structures. Computational and experimental methods indicate that the addition of perfluorinated aromatic linkers in the assembly of porous organic cages opens up new possibilities for influencing the reaction pathway towards rare and unknown structures.

Stochastic thermodynamics is formulated under the assumption of perfect knowledge of all thermodynamic parameters. However, in any real-world situation, there is nonzero 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 effective scenario, we fix the (unknown, randomly generated) parameters of an experimental apparatus and then repeatedly observe (stochastic) trajectories of the system for that fixed apparatus. In contrast, in the (consistently with the effective scenario) phenomenological scenario, the (unknown) apparatus is re-generated for each trajectory. We derive expressions for thermodynamic quantities in both scenarios. For the effective scenario, we also discuss the physical interpretation of entropy production (EP) and derive the mismatch cost. To illustrate this scenario, we also provide a numerical analysis of the thermodynamics of a quantum dot implementing bit erasure with uncertain temperature. We also analyze the protocol for changing the distribution over states in a way that maximizes work extraction, again in the effective scenario. 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 integral 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. Our results provide a very preliminary investigation of the myriad issues that arise when one tries to expand stochastic thermodynamics to account for uncertainty in the parameters governing a physical process.

Many dynamical systems consist of multiple, co-evolving subsystems (i.e., they have multiple degrees of freedom). Often, the dynamics of one or more of these subsystems will not directly depend on the state of some other subsystems, resulting in a network of dependencies governing the dynamics. How does this dependency network affect the full system’s thermodynamics? Prior studies on the stochastic thermodynamics of multipartite processes have addressed this question by assuming that, in addition to the constraints of the dependency network, only one subsystem is allowed to change state at a time. However, in many real systems, such as chemical reaction networks or electronic circuits, multiple subsystems can—or must—change state together. Here, we investigate the thermodynamics of such composite processes, in which multiple subsystems are allowed to change state simultaneously. We first present new, strictly positive lower bounds on entropy production in composite processes. We then present thermodynamic uncertainty relations for information flows in composite processes. We end with strengthened speed limits for composite processes.

The Seshat database has made it possible to reveal large-scale patterns in human cultural evolution. Here, Shin et al. investigate transitions in social complexity and find alternating thresholds of polity size and information processing required for further sociopolitical development.

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.

Deterministic maps from initial to final states can always be modelled using the master equation formalism, provided additional “hidden” states are available. Here, the authors demonstrate a tradeoff between the required number of such states and the number of required, suitably defined “hidden time steps”.

In many real-world situations, there are constraints on the ways in which a physical system can be manipulated. We investigate the entropy production (EP) and extractable work involved in bringing a system from some initial distribution p to some final distribution p^{′}, given that the set of master equations available to the driving protocol obeys some constraints. We first derive general bounds on EP and extractable work, as well as a decomposition of the nonequilibrium free energy into an “accessible free energy” (which can be extracted as work, given a set of constraints) and an “inaccessible free energy” (which must be dissipated as EP). In a similar vein, we consider the thermodynamics of information in the presence of constraints and decompose the information acquired in a measurement into “accessible” and “inaccessible” components. This decomposition allows us to consider the thermodynamic efficiency of different measurements of the same system, given a set of constraints. We use our framework to analyze protocols subject to symmetry, modularity, and coarse-grained constraints and consider various examples including the Szilard box, the 2D Ising model, and a multiparticle flashing ratchet.

We extend stochastic thermodynamics by relaxing the two assumptions that the Markovian dynamics must be linear and that the equilibrium distribution must be a Boltzmann distribution. We show that if we require the second law to hold when those assumptions are relaxed, then it cannot be formulated in terms of Shannon entropy. However, thermodynamic consistency is salvaged if we reformulate the second law in terms of generalized entropy; our first result is an equation relating the precise form of the non-linear master equation to the precise associated generalized entropy which results in thermodynamic consistency. We then build on this result to extend the usual trajectory-level definitions of thermodynamic quantities that are appropriate even when the two assumptions are relaxed. We end by using these trajectory-level definitions to derive extended versions of the Crooks fluctuation theorem and Jarzynski equality which apply when the two assumptions are relaxed.

Turing machines (TMs) are the canonical model of computation in computer science and physics. We combine techniques from algorithmic information theory and stochastic thermodynamics to analyze the thermodynamic costs of TMs. We consider two different ways of realizing a given TM with a physical process. The first realization is designed to be thermodynamically reversible when fed with random input bits. The second realization is designed to generate less heat, up to an additive constant, than any realization that is computable (i.e., consistent with the physical Church-Turing thesis). We consider three different thermodynamic costs: The heat generated when the TM is run on each input (which we refer to as the “heat function”), the minimum heat generated when a TM is run with an input that results in some desired output (which we refer to as the “thermodynamic complexity” of the output, in analogy to the Kolmogorov complexity), and the expected heat on the input distribution that minimizes entropy production. For universal TMs, we show for both realizations that the thermodynamic complexity of any desired output is bounded by a constant (unlike the conventional Kolmogorov complexity), while the expected amount of generated heat is infinite. We also show that any computable realization faces a fundamental trade-off among heat generation, the Kolmogorov complexity of its heat function, and the Kolmogorov complexity of its input-output map. We demonstrate this trade-off by analyzing the thermodynamics of erasing a long string.

Many systems are composed of multiple, interacting subsystems, where the dynamics of each subsystem only depends on the states of a subset of the other subsystems, rather than on all of them. I analyze how such constraints on the dependencies of each subsystem’s dynamics affects the thermodynamics of the overall, composite system. Specifically, I derive a strictly nonzero lower bound on the minimal achievable entropy production rate of the overall system in terms of these constraints. The bound is based on constructing counterfactual rate matrices, in which some subsystems are held fixed while the others are allowed to evolve. This bound is related to the ‘learning rate’ of stationary bipartite systems, and more generally to the ‘information flow’ in bipartite systems. It can be viewed as a strengthened form of the second law, applicable whenever there are constraints on which subsystem within an overall system can directly affect which other subsystem.

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 the 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.

The original version of the Supplementary Information associated with this Article contained an error throughout in which all inline references to Theorems, Definitions and Lemmas given in the main Article were incorrectly given as ‘??’. The HTML has been updated to include a corrected version of the Supplementary Information.