Off-lattice active Brownian particles form clusters and undergo phase separation even in the absence of attractions or velocity-alignment mechanisms. Arguments that explain this phenomenon appeal only to the ability of particles to move persistently in a direction that fluctuates, but existing lattice models of hard particles that account for this behavior do not exhibit phase separation. Here we present a lattice model of active matter that exhibits motility-induced phase separation in the absence of velocity alignment. Using direct and rare-event sampling of dynamical trajectories, we show that clustering and phase separation are accompanied by pronounced fluctuations of static and dynamic order parameters. This model provides a complement to off-lattice models for the study of motility-induced phase separation.

The equations of hydrodynamics including mass, linear momentum, angular momentum, and energy are derived by coarse-graining the microscopic equations of motion for systems consisting of rotary dumbbells driven by internal torques. In deriving the balance of linear momentum, we find that the symmetry of the stress tensor is broken due to the presence of non-zero torques on individual particles. The broken symmetry of the stress tensor induces internal spin in the fluid and leads us to consider the balance of internal angular momentum in addition to the usual moment of momentum. In the absence of spin, the moment of momentum is the same as the total angular momentum. In deriving the form of the balance of total angular momentum, we find the microscopic expressions for the couple stress tensor that drives the spin field. We show that the couple stress contains contributions from both intermolecular interactions and the active forces. The presence of spin leads to the idea of balance of moment of inertia due to the constant exchange of particles in a small neighborhood around a macroscopic point. We derive the associated balance of moment of inertia at the macroscale and identify the moment of inertia flux that induces its transport. Finally, we obtain the balances of total and internal energy of the active fluid and identify the sources of heat and heat fluxes in the system.

Key to biological success, the requisite variety that confronts an adaptive organism is the set of detectable, accessible, and controllable states in its environment. We analyze its role in the thermodynamic functioning of information ratchets---a form of autonomous Maxwellian Demon capable of exploiting fluctuations in an external information reservoir to harvest useful work from a thermal bath. This establishes a quantitative paradigm for understanding how adaptive agents leverage structured thermal environments for their own thermodynamic benefit. General ratchets behave as memoryful communication channels, interacting with their environment sequentially and storing results to an output. The bulk of thermal ratchets analyzed to date, however, assume memoryless environments that generate input signals without temporal correlations. Employing computational mechanics and a new information-processing Second Law of Thermodynamics (IPSL) we remove these restrictions, analyzing general finite-state ratchets interacting with structured environments that generate correlated input signals. On the one hand, we demonstrate that a ratchet need not have memory to exploit an uncorrelated environment. On the other, and more appropriate to biological adaptation, we show that a ratchet must have memory to most effectively leverage structure and correlation in its environment. The lesson is that to optimally harvest work a ratchet's memory must reflect the input generator's memory. Finally, we investigate achieving the IPSL bounds on the amount of work a ratchet can extract from its environment, discovering that finite-state, optimal ratchets are unable to reach these bounds. In contrast, we show that infinite-state ratchets can go well beyond these bounds by utilizing their own infinite "negentropy". We conclude with an outline of the collective thermodynamics of information-ratchet swarms.

Information processing typically occurs via the composition of modular units, such as the universal logic gates found in discrete computation circuits. The benefit of modular information processing, in contrast to globally integrated information processing, is that complex computations are more easily and flexibly implemented via a series of simpler, localized information processing operations that only control and change local degrees of freedom. We show that, despite these benefits, there are unavoidable thermodynamic costs to modularity - costs that arise directly from the operation of localized processing and that go beyond Landauer's bound on the work required to erase information. Localized operations are unable to leverage global correlations, which are a thermodynamic fuel. We quantify the minimum irretrievable dissipation of modular computations in terms of the difference between the change in global nonequilibrium free energy, which captures these global correlations, and the local (marginal) change in nonequilibrium free energy, which bounds modular work production. This modularity dissipation is proportional to the amount of additional work required to perform a computational task modularly, measuring a structural energy cost. It determines the thermodynamic efficiency of different modular implementations of the same computation, and so it has immediate consequences for the architecture of physically embedded transducers, known as information ratchets. Constructively, we show how to circumvent modularity dissipation by designing internal ratchet states that capture the information reservoir's global correlations and patterns. Thus, there are routes to thermodynamic efficiency that circumvent globally integrated protocols and instead reduce modularity dissipation to optimize the architecture of computations composed of a series of localized operations.

Key to biological success, the requisite variety that confronts an adaptive organism is the set of detectable, accessible, and controllable states in its environment. We analyze its role in the thermodynamic functioning of information ratchets—a form of autonomous Maxwellian Demon capable of exploiting fluctuations in an external information reservoir to harvest useful work from a thermal bath. This establishes a quantitative paradigm for understanding how adaptive agents leverage structured thermal environments for their own thermodynamic benefit. General ratchets behave as memoryful communication channels, interacting with their environment sequentially and storing results to an output. The bulk of thermal ratchets analyzed to date, however, assume memoryless environments that generate input signals without temporal correlations. Employing computational mechanics and a new information-processing Second Law of Thermodynamics (IPSL) we remove these restrictions, analyzing general finite-state ratchets interacting with structured environments that generate correlated input signals. On the one hand, we demonstrate that a ratchet need not have memory to exploit an uncorrelated environment. On the other, and more appropriate to biological adaptation, we show that a ratchet must have memory to most effectively leverage structure and correlation in its environment. The lesson is that to optimally harvest work a ratchet’s memory must reflect the input generator’s memory. Finally, we investigate achieving the IPSL bounds on the amount of work a ratchet can extract from its environment, discovering that finite-state, optimal ratchets are unable to reach these bounds. In contrast, we show that infinite-state ratchets can go well beyond these bounds by utilizing their own infinite “negentropy”. We conclude with an outline of the collective thermodynamics of information-ratchet swarms.

We reply to arXiv:1508.00203 `Comment on "Identifying Functional Thermodynamics in Autonomous Maxwellian Ratchets" (arXiv:1507.01537v2)'.

Information engines can use structured environments as a resource to generate work by randomizing ordered inputs and leveraging the increased Shannon entropy to transfer energy from a thermal reservoir to a work reservoir. We give a broadly applicable expression for the work production of an information engine, generally modeled as a memoryful channel that communicates inputs to outputs as it interacts with an evolving environment. The expression establishes that an information engine must have more than one memory state in order to leverage input environment correlations. To emphasize this functioning, we designed an information engine powered solely by temporal correlations and not by statistical biases, as employed by previous engines. Key to this is the engine's ability to synchronize---the engine automatically returns to a desired dynamical phase when thrown into an unwanted, dissipative phase by corruptions in the input---that is, by unanticipated environmental fluctuations. This self-correcting mechanism is robust up to a critical level of corruption, beyond which the system fails to act as an engine. We give explicit analytical expressions for both work and critical corruption level and summarize engine performance via a thermodynamic-function phase diagram over engine control parameters. The results reveal a new thermodynamic mechanism based on nonergodicity that underlies error correction as it operates to support resilient engineered and biological systems.

Information engines can use structured environments as a resource to generate work by randomizing ordered inputs and leveraging the increased Shannon entropy to transfer energy from a thermal reservoir to a work reservoir. We give a broadly applicable expression for the work production of an information engine, generally modeled as a memoryful channel that communicates inputs to outputs as it interacts with an evolving environment. The expression establishes that an information engine must have more than one memory state in order to leverage input environment correlations. To emphasize this functioning, we designed an information engine powered solely by temporal correlations and not by statistical biases, as employed by previous engines. Key to this is the engine's ability to synchronize-the engine automatically returns to a desired dynamical phase when thrown into an unwanted, dissipative phase by corruptions in the input-that is, by unanticipated environmental fluctuations. This self-correcting mechanism is robust up to a critical level of corruption, beyond which the system fails to act as an engine. We give explicit analytical expressions for both work and critical corruption level and summarize engine performance via a thermodynamic-function phase diagram over engine control parameters. The results reveal a thermodynamic mechanism based on nonergodicity that underlies error correction as it operates to support resilient engineered and biological systems.

We introduce a family of Maxwellian Demons for which correlations among information bearing degrees of freedom can be calculated exactly and in compact analytical form. This allows one to precisely determine Demon functional thermodynamic operating regimes, when previous methods either misclassify or simply fail due to approximations they invoke. This reveals that these Demons are more functional than previous candidates. They too behave either as engines, lifting a mass against gravity by extracting energy from a single heat reservoir, or as Landauer erasers, consuming external work to remove information from a sequence of binary symbols by decreasing their individual uncertainty. Going beyond these, our Demon exhibits a new functionality that erases bits not by simply decreasing individual-symbol uncertainty, but by increasing inter-bit correlations (that is, by adding temporal order) while increasing single-symbol uncertainty. In all cases, but especially in the new erasure regime, exactly accounting for informational correlations leads to tight bounds on Demon performance, expressed as a refined Second Law of thermodynamics that relies on the Kolmogorov-Sinai entropy for dynamical processes and not on changes purely in system configurational entropy, as previously employed. We rigorously derive the refined Second Law under minimal assumptions and so it applies quite broadly - for Demons with and without memory and input sequences that are correlated or not. We note that general Maxwellian Demons readily violate previously proposed, alternative such bounds, while the current bound still holds. As such, it broadly describes the minimal energetic cost of any computation by a thermodynamic system.

A central result that arose in applying information theory to the stochastic thermodynamics of nonlinear dynamical systems is the Information-Processing Second Law (IPSL): the physical entropy of the universe can decrease if compensated by the Shannon-Kolmogorov-Sinai entropy change of appropriate information-carrying degrees of freedom. In particular, the asymptotic-rate IPSL precisely delineates the thermodynamic functioning of autonomous Maxwellian demons and information engines. How do these systems begin to function as engines, Landauer erasers, and error correctors? Here, we identify a minimal, inescapable transient dissipation engendered by physical information processing not captured by asymptotic rates, but critical to adaptive thermodynamic processes such as found in biological systems. A component of transient dissipation, we also identify an implementation-dependent cost that varies from one physical substrate to another for the same information processing task. Applying these results to producing structured patterns from a structureless information reservoir, we show that "retrodictive" generators achieve the minimal costs. The results establish the thermodynamic toll imposed by a physical system's structure as it comes to optimally transduce information.