Bulletin of the American Physical Society
APS March Meeting 2022
Volume 67, Number 3
Monday–Friday, March 14–18, 2022; Chicago
Session Y09: Stochastic Thermodynamics of Biological and Artificial Information Processing IIFocus Recordings Available
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Sponsoring Units: GSNP Chair: David Wolpert, Santa Fe Institute Room: McCormick Place W-180 |
Friday, March 18, 2022 8:00AM - 8:36AM |
Y09.00001: Entropy generation during computation - is it really avoidable, even in principle? Invited Speaker: Thomas E Ouldridge Recent years have seen a resurgence in interest in minimising the thermodynamic costs of computation, driven both by underpinning advances in stochastic thermodynamics and increasing focus on energy efficiency in all aspects of life. In principle, any operation can be performed in a thermodynamically reversible manner. However, there are a number of challenges associated with performing anything complex enough to be reasonably described as a "computation" when one considers even a highly idealised physical instantiation of the computing device. In this talk I will illustrate these ideas through concrete models of two systems: one that can perform online learning and another capable of universal computation. These models demonstrate the thermodynamic consequences of over-fitting to sampling noise, learning on the fly with finite memory, and the variable halting times of Turing machines. Furthermore, we use these approaches to argue that, although logical reversibility of an operation is not strictly required for thermodynamic reversibility, it is effectively necessary when performing those operations are complex. |
Friday, March 18, 2022 8:36AM - 8:48AM |
Y09.00002: Thermodynamic uncertainty relations and first-passage times for information flows in co-evolving systems Farita Tasnim, Tarek Tohme, David H Wolpert Many systems are composed of multiple co-evolving subsystems. Information flowing between those subsystems can be quantified, with an information-theoretic measure of how much each subsystem affects the dynamics of the others, on average. This "information flow" has been shown to affect how much each subsystem's interactions with the others contributes to the global entropy production rate. Here, we introduce trajectory-level information flows, as well as conditional information flows. As we show, in a non-equilibrium steady state (NESS), these flows are currents, and therefore subject to the thermodynamic uncertainty relations. Therefore the statistical precision of the information flows across a system in an NESS are bounded by local and global entropy productions. We also investigate the thermodynamic properties of first-passage times for these inter-subsystem information flows. Finally, we derive relations between information flows and other measures of correlation among subsystems, such as the inclusion-exclusion information and multi-divergence. |
Friday, March 18, 2022 8:48AM - 9:00AM |
Y09.00003: Fluid intelligence: activity from learning and forgetting Bryan VanSaders, Vincenzo Vitelli Active systems ranging from cellular colonies to collections of nanomotors typically derive their unusual hydrodynamic properties from the exertion of mechanical work at small scales. However, when the microscopic constituents can record measurements of their environment, thermodynamics becomes inextricably intertwined with information processing. To single-out how information processing affects the dynamics of active fluids, we propose a model system in which the microscopic constituents reach non-equilibrium steady states by taking measurements of their surroundings and performing zero-work actions which exploit that information. Using molecular dynamics simulations, kinetic theory and hydrodynamics we explore the properties of this class of many-body Maxwell-demon systems. Furthermore, we employ reinforcement learning to explore goal-oriented policies of constituent behavior and find that this form of information-based activity is robust even when the agitating environment is athermal. Our model system is illustrative of a broader class of active systems in which intelligent actors choose low-effort actions that exploit environmental fluctuations to achieve nonequilibrium states. |
Friday, March 18, 2022 9:00AM - 9:12AM |
Y09.00004: The nonequilibrium dynamics of a temporally responsive, single-molecule automaton Zhongmin Zhang, Zhiyue Lu Molecules with multiple meta-stable configurations on rough energy landscapes could demonstrate complex hysteresis responses to various temporally changing environments. We argue that such nonequilibrium hysteresis responses could allow a molecule to recognize, memorize, and respond specifically to temporal patterns of a changing environment. Moreover, such molecules could be steered into far-from-equilibrium configurations if the environment is programmed to change according to specific protocols. We demonstrate both behaviors in a simple solvable model of a linear polymer chain with a temporally controlled end-to-end distance λ(t). A polymer consisting of N foldable segments is modeled by a novel dual-rate master equation over the 2N possible configurations. With an asymmetric energy landscape for folding/unfolding, we designed a polymer that can function as a molecular timer and temporal pattern recorder. Moreover, we discovered that the evolution of the dominant configuration of the molecule acts like an automaton, which allows us to design driving protocols to steer the molecule into nonequilibrium distributions dominated by any desired configuration. |
Friday, March 18, 2022 9:12AM - 9:24AM |
Y09.00005: Energetically optimal strategies in reactive-diffusive signaling Samuel J Bryant, Benjamin B Machta In biological processing networks, it is often necessary to move a signal between the output of one processing step to the input of the next. Many different physical schemes have evolved to send signals over physical distances for this purpose. We can compare different signaling schemes by computing their associated energetic costs, measured in Joules per bit, obtained by calculating the rate of information transfer and the corresponding energy dissipation. Perhaps the most common of these schemes in biology is diffusive signaling. In a diffusive signaling network, a sender molecule produces second messengers which travel through the cytoplasm where their concentration is measured by a receiver molecule. Here we present a general strategy of reactive-diffusive signaling that minimizes this cost per bit by colocalizing the enzyme responsible for deactivating messengers with the sender itself. Despite the increased dissipation caused by futile activation-deactivation cycles, the overall cost per bit decreases. While this is a general phenomena, we suggest that this explains the colocalization of the kinase CheA and phosphotase CheZ in the E. coli chemotactic cascade. |
Friday, March 18, 2022 9:24AM - 9:36AM |
Y09.00006: Dissipation-Accuracy-Speed tradeoffs in computations executed via on-lattice self-assembly Jonah Greenberg Computations are subject to thermodynamic constraints. In particular, there exist fundamental trade-offs between the accuracy, speed, and dissipation of information-processing systems. We investigate such relationships in an experimentally inspired model of a molecular computer. This model computes programmable Boolean circuits through the self-assembly dynamics of information-bearing DNA tiles. Data from simulations suggests the existence of a tradeoff between speed, accuracy, and dissipation. In particular, high-accuracy computations necessitate both a large dissipation and an increased speed. We will discuss the nature of these dissipation-accuracy-speed tradeoffs, as well as the dependence of these tradeoffs on the complexity of the Boolean circuit being executed. |
Friday, March 18, 2022 9:36AM - 9:48AM |
Y09.00007: A Bayesian mechanics for adaptive systems Lancelot Da Costa We develop a Bayesian mechanics for adaptive systems. This mechanics has the same starting point as quantum, statistical and classical mechanics. The only difference is that careful attention is paid to the way that the states internal to something interface with the states external to it. |
Friday, March 18, 2022 9:48AM - 10:00AM |
Y09.00008: Erasing a bit with zero work cost by bypassing Liouville's theorem Roi Holtzman, Oren Raz, Geva Arwas The celebrated Landauer bound is the fundamental universal cost of computation: there must be dissipation of at least kBTlog2 per erasure of one bit. This result suggests that no closed Hamiltonian system can be used to encode a useful bit. Indeed, bit erasure amounts to concentrating the probability distribution in phase space, and Liouville's theorem forbids such concentration for Hamiltonian systems. However, when the system is confined to a set of measure zero, Liouville's theorem is no longer a restriction. |
Friday, March 18, 2022 10:00AM - 10:12AM |
Y09.00009: Stochastic Thermodynamics of Finite Automata Gülce Kardes, David H Wolpert The deterministic finite automaton (DFA) is a foundational model of computation. It is implemented by digital computational systems ranging from circuits to compilers, and is ubiquitous in biological systems. The state space of a DFA consists of a set of internal states, strings of input symbols, and a pointer indicating the current input symbol. The complexity of a DFA is its number of internal states. Here we investigate the stochastic thermodynamics of running a DFA, using an inclusive, Hamiltonian formulation, in which we partition the DFA's state space into a system of interest (SOI) and a separate environment. In the first partition, the SOI is the pointer and the DFA's internal state. We prove that in any set of DFAs that behave equivalently, the DFA with minimal complexity is the one with the least entropy production. This result holds for every iteration of the DFA, and for any distribution over input strings. In the second partition, the SOI is the pointer, the internal state, and the current symbol. Under this partition, the DFA is formally identical to a Markov information source. We exploit this to establish a set of results on the thermodynamics of block codes for information sources. |
Friday, March 18, 2022 10:12AM - 10:24AM |
Y09.00010: Nonequilibrium thermodynamics of uncertain stochastic processes Jan Korbel, David H Wolpert In real-world stochastic thermodynamics, we never have infinitely > precise knowledge of the temperatures / chemical potentials of the reservoirs, the energy spectrum, the control protocol, maybe even the number of reservoirs, etc. We investigate how such uncertainty about the precise experimental apparatus modifies the laws of stochastic thermodynamics. We first consider the case where you sample a given distribution over apparatus' once and then sample the distribution over trajectories conditioned on that apparatus an infinite number of times. This uncovers both commonalities and differences between the stochastic thermodynamics of systems with an uncertain apparatus and standard (full certainty) stochastic thermodynamics. We next consider the case where we sample an apparatus once and then generate a sequence of multiple random trajectories where we are able to modify some aspects of the apparatus from one trajectory to the next, based on information concerning the apparatus provided by the earlier trajectories. This opens a very rich set of issues concerning the thermodynamic value of information about an apparatus, extending previous work in the literature on the thermodynamic value of information about the state of the system. |
Friday, March 18, 2022 10:24AM - 10:36AM |
Y09.00011: Cellular costs in the synthesis of glycan information Alkesh Yadav, Garud Iyengar, Madan Rao Many proteins that undergo sequential enzymatic modification in the Golgi cisternae are displayed at the plasma membrane as cell identity markers. The modified proteins, called glycans, represent a molecular code. The fidelity of this glycan code is measured by how accurately the glycan synthesis machinery realises the desired target glycan distribution for a particular cell type and niche. In an earlier work, we brought out the tradeoffs in number of Golgi cisternae, number of glycosylation enzymes and their specificity, required to synthesize a prescribed complex target glycan distribution within a given fidelity. In this work we study how non equilibrium driving in transport and reaction rates affect fidelity of the synthesized glycan distribution. |
Friday, March 18, 2022 10:36AM - 10:48AM |
Y09.00012: Stochastic thermodynamics of anomalous diffusion generated by scaled and fractional Brownian motions Seyed Mohsen Jebreiil Khadem, Sabine H. L. Klapp, Rainer Klages We study stochastic thermodynamics for non-equilibrium systems that can exhibit anomalous diffusion with the main focus on deriving an integral fluctuation relation (IFR) for the total entropy production. The dynamics of those systems are described by (i) Markovian processes with a time-dependent diffusivity such as scaled Brownian motion and (ii) non-Markovian fractional Brownian motion. The former case is an immediate generalization of normal diffusion which is used here mainly, first, to generalize the definitions of the thermodynamic quantities such as heat, work and entropy production along a single trajectory and, second, to revisit the derivation of the IFR for the total entropy production by considering that the fluctuation-dissipation relation may or may not be valid. In the latter case, we investigate how the non-Markovian feature of the dynamics alters the conventional notion of stochastic thermodynamics by leading to a violation of the IFR for the total entropy production. We demonstrate that, such a violation can be circumvented by formally defining a temperature functional that fulfils a general form of fluctuation-dissipation relation. Using a perturbation method, we calculate the first two leading terms of the temperature functional. Our perturbative analysis also unravels that the origin of that violation can be tracked to a generalized form of a heat exchange between the system and the environment. We obtain an analytical expression for the generalized heat function and provide a physically meaningful interpretation by introducing the concepts of retarded force and retarded velocity that include the impact of the memory of the environment. |
Friday, March 18, 2022 10:48AM - 11:00AM |
Y09.00013: Optimality in biological proofreading SHRABANI MONDAL Biological processes such as DNA replication, RNA transcription, and protein translation show remarkable speed and accuracy in selecting the right substrate from pools of chemically identical molecules. This result is obtained by a nonequilibrium error-reduction mechanism called kinetic proofreading (KPR). The KPR mechanism enhances the accuracy of the biological process at the cost of higher energy dissipation and reduced speed. Hence, there is a trade-off between speed, error, and dissipation. The second law of thermodynamics sets fundamental bounds on speed, error, and dissipation of replicating enzymes. Despite their theoretical interest, these bounds are usually far from the operating regimes of replicating enzymes. This motivates us to formulate the optimality principles for speed, error, and dissipation using concepts from mathematical optimization theory. |
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