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Non-equilibrium behaviour of information-processing systems with computational constraints

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Grau-Moya,  J
Dept. Empirical Inference, Max Planck Institute for Intelligent Systems, Max Planck Society;
Research Group Sensorimotor Learning and Decision-Making, Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Braun,  DA
Research Group Sensorimotor Learning and Decision-Making, Max Planck Institute for Biological Cybernetics, Max Planck Society;
Research Group Sensorimotor Learning and Decision-making, Max Planck Institute for Intelligent Systems, Max Planck Society;

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Citation

Grau-Moya, J., Krueger, M., & Braun, D. (2015). Non-equilibrium behaviour of information-processing systems with computational constraints. Poster presented at Workshop on Recent Developments In Non-Equilibrium Physics "Luxembourg out of Equilibrium", Luxembourg, Luxembourg.


Cite as: http://hdl.handle.net/11858/00-001M-0000-002A-47A5-F
Abstract
Living organisms from single cells to humans need to adapt continuously to respond to changes in their environment. This process of adaptation of behaviour—from ”simple” regulation of temperature to more complex processes of decision-making can be thought of as improvements in performance according to some fitness function. Here we consider an abstract model of organisms as decision-makers with limited information-processing resources that trade off between maximization of utility (performance) and computational costs measured by a relative entropy. Isothermal thermodynamic systems formally undergo the same trade-off when subject to changes in their surrounding (e.g. the appearance of a magnetic field). Such systems minimize the free energy to reach equilibrium states that balance internal energy and entropic cost. When there is a fast change in the environment these systems evolve in a non-equilibrium fashion because they are unable to follow exactly the path of equilibrium distributions. In this situation the work spent to change the thermodynamic system is greater than the free energy. Similarly, the utility of an organism in a fast changing environment is less than the optimal utility it could obtain if it could adapt instantaneously. We quantify the relation between performance losses during adaptation processes and the computational capabilities of decision-makers. We discuss how non-equilibrium equalities like the Jarzynski equation and Crooks’ fluctuation theorem hold both for physical systems and abstract decision makers.