A space-time tradeoff for implementing a function with master equation dynamics

Machine learning at the mesoscale: A computation-dissipation bottleneck

The cost of information processing in physical systems calls for a trade-off between performance and energetic expenditure. Here we formulate and study a computation-dissipation bottleneck in mesoscopic systems used as input-output devices. Using both real data sets and synthetic tasks, we show how nonequilibrium leads to enhanced performance. Our framework sheds light on a crucial compromise between information compression, input-output computation and dynamic irreversibility induced by nonreciprocal interactions.

Birth-death-suppression Markov process and wildfires

Birth and death Markov processes can model stochastic physical systems from percolation to disease spread and, in particular, wildfires. We introduce and analyze a birth-death-suppression Markov process as a model of controlled culling of an abstract, dynamic population. Using analytic techniques, we characterize the probabilities and timescales of outcomes like absorption at zero (extinguishment) and the probability of the cumulative population (burned area) reaching a given size. The latter requires control over the embedded Markov chain: this discrete process is solved using the Pollazcek orthogonal polynomials, a deformation of the Gegenbauer/ultraspherical polynomials. This allows analysis of processes with bounded cumulative population, corresponding to finite burnable substrate in the wildfire interpretation, with probabilities represented as spectral integrals. This technology is developed to lay the foundations for a dynamic decision support framework. We devise real-time risk metrics and suggest future directions for determining optimal suppression strategies, including multievent resource allocation problems and potential applications for reinforcement learning.

Information Engine in a Nonequilibrium Bath

Information engines can convert thermal fluctuations of a bath at temperature T into work at rates of order k_{B}T per relaxation time of the system. We show experimentally that such engines, when in contact with a bath that is out of equilibrium, can extract much more work. We place a heavy, micron-scale bead in a harmonic potential that ratchets up to capture favorable fluctuations. Adding a fluctuating electric field increases work extraction up to ten times, limited only by the strength of the applied field. Our results connect Maxwell's demon with energy harvesting and demonstrate that information engines in nonequilibrium baths can greatly outperform conventional engines.

Probing the theoretical and computational limits of dissipative design

Self-assembly, the process by which interacting components form well-defined and often intricate structures, is typically thought of as a spontaneous process arising from equilibrium dynamics. When a system is driven by external nonequilibrium forces, states statistically inaccessible to the equilibrium dynamics can arise, a process sometimes termed direct self-assembly. However, if we fix a given target state and a set of external control variables, it is not well-understood (i) how to design a protocol to drive the system toward the desired state nor (ii) the cost of persistently perturbing the stationary distribution. In this work, we derive a bound that relates the proximity to the chosen target with the dissipation associated with the external drive, showing that high-dimensional external control can guide systems toward target distribution but with an inevitable cost. Remarkably, the bound holds arbitrarily far from equilibrium. Second, we investigate the performance of deep reinforcement learning algorithms and provide evidence for the realizability of complex protocols that stabilize otherwise inaccessible states of matter.

Entropy production given constraints on the energy functions

We consider the problem of driving a finite-state classical system from some initial distribution p to some final distribution p^{'} with vanishing entropy production (EP), under the constraint that the driving protocols can only use some limited set of energy functions E. Assuming no other constraints on the driving protocol, we derive a simple condition that guarantees that such a transformation can be carried out, which is stated in terms of the smallest probabilities in {p,p^{'}} and a graph-theoretic property defined in terms of E. Our results imply that a surprisingly small amount of control over the energy function is sufficient (in particular, any transformation p→p^{'} can be carried out as soon as one can control some one-dimensional parameter of the energy function, e.g., the energy of a single state). We also derive a lower bound on the EP under more general constraints on the transition rates, which is formulated in terms of a convex optimization problem.

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.