Entropy balance and Information processing in bipartite and non-bipartite composite systems

Abstract

Information dynamics is an emerging description of information processing in complex systems which describes systems in terms of intrinsic computation, identifying computational primitives of information storage and transfer. In this paper we make a formal analogy between information dynamics and stochastic thermodynamics which describes the thermal behaviour of small irreversible systems. As stochastic dynamics is increasingly being utilized to quantify the thermodynamics associated with the processing of information we suggest such an analogy is instructive, highlighting that existing thermodynamic quantities can be described solely in terms of extant information theoretic measures related to information processing. In this contribution we construct irreversibility measures in terms of these quantities and relate them to the physical entropy productions that characterise the behaviour of single and composite systems in stochastic thermodynamics illustrating them with simple examples. Moreover, we can apply such a formalism to systems which do not have a bipartite structure. In particular we demonstrate that, given suitable non-bipartite processes, the heat flow in a subsystem can still be identified and one requires the present formalism to recover generalizations of the second law. In these systems residual irreversibility is associated with neither subsystem and this must be included in the these generalised second laws. This opens up the possibility of describing all physical systems in terms of computation allowing us to propose a framework for discussing the reversibility of systems traditionally out of scope of stochastic thermodynamics.

28 pages, 4 figures

References in corpus (18)

• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• Second Law of Thermodynamics with Discrete Quantum Feedback Control
• Work and information processing in a solvable model of Maxwell's demon
• Local information transfer as a spatiotemporal filter for complex systems
• The thermodynamics of prediction
• Thermodynamics of a physical model implementing a Maxwell demon
• Nonequilibrium Detailed Fluctuation Theorem for Repeated Discrete Feedback
• Integral fluctuation theorem for the housekeeping heat
• Maxwell's demon in biochemical signal transduction with feedback loop
• Second-law-like inequalities with information and their interpretations
• Fluctuation Relations for Diffusion Processes
• The Organization of Intrinsic Computation: Complexity-Entropy Diagrams and the Diversity of Natural Information Processing
• Stochastic thermodynamics for "Maxwell demon" feedbacks
• Stochastic thermodynamics with information reservoirs
• Transfer entropy in continuous time, with applications to jump and neural spiking processes
• The thermodynamic efficiency of computations made in cells across the range of life
• Biochemical machines for the interconversion of mutual information and work
• Local Detailed Balance : A Microscopic Derivation

Cited by in corpus (3)

• Thermodynamics of emergent structure in active matter
• Detailed Fluctuation Relation for Arbitrary Measurement and Feedback Schemes
• Information thermodynamics for interacting stochastic systems without bipartite structure