TITLE

An Information Theory Approach to Nonlinear, Nonequilibrium Thermodynamics

AUTHOR(S)
Rogers, David; Beck, Thomas; Rempe, Susan
PUB. DATE
October 2011
SOURCE
Journal of Statistical Physics;Oct2011, Vol. 145 Issue 2, p385
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
Using the problem of ion channel thermodynamics as an example, we illustrate the idea of building up complex thermodynamic models by successively adding physical information. We present a new formulation of information algebra that generalizes methods of both information theory and statistical mechanics. From this foundation we derive a theory for ion channel kinetics, identifying a nonequilibrium 'process' free energy functional in addition to the well-known integrated work functionals. The Gibbs-Maxwell relation for the free energy functional is a Green-Kubo relation, applicable arbitrarily far from equilibrium, that captures the effect of non-local and time-dependent behavior from transient thermal and mechanical driving forces. Comparing the physical significance of the Lagrange multipliers to the canonical ensemble suggests definitions of nonequilibrium ensembles at constant capacitance or inductance in addition to constant resistance. Our result is that statistical mechanical descriptions derived from a few primitive algebraic operations on information can be used to create experimentally-relevant and computable models. By construction, these models may use information from more detailed atomistic simulations. Two surprising consequences to be explored in further work are that (in)distinguishability factors are automatically predicted from the problem formulation and that a direct analogue of the second law for thermodynamic entropy production is found by considering information loss in stochastic processes. The information loss identifies a novel contribution from the instantaneous information entropy that ensures non-negative loss.
ACCESSION #
67186754

 

Related Articles

  • Thermodynamic and stochastic theory of nonequilibrium systems: A Lagrangian approach to fluctuations and relation to excess work. Suárez, Alberto; Ross, John; Peng, Bo; Hunt, Katharine L. C.; Hunt, Paul M. // Journal of Chemical Physics;3/15/1995, Vol. 102 Issue 11, p4563 

    The dynamics of fluctuations in systems approaching a nonequilibrium steady state, with or without detailed balance, are investigated by means of a Lagrangian function, which is derived from the generator of time displacement (Hamiltonian) of the mesoscopic evolution equation. In the...

  • Operational derivation of Boltzmann distribution with Maxwell's demon model. Hosoya, Akio; Maruyama, Koji; Shikano, Yutaka // Scientific Reports;11/27/2015, p17011 

    The resolution of the Maxwell's demon paradox linked thermodynamics with information theory through information erasure principle. By considering a demon endowed with a Turing-machine consisting of a memory tape and a processor, we attempt to explore the link towards the foundations of...

  • Communication: Length scale dependent oil-water energy fluctuations. Underwood, Robin; Ben-Amotz, Dor // Journal of Chemical Physics;Nov2011, Vol. 135 Issue 20, p201102 

    Interfacial fluctuations in the cohesive (van der Waals) interaction energy of spherical oil-drops with water provide evidence of a length scale dependent transition from linear to non-linear response behavior. For sub-nanometer oil-drop sizes, energy fluctuations are found to be independent of...

  • An Isobaric–Isothermal Ensemble in Statistical Mechanics. Magomedov, K. M. // Doklady Physics;Aug2000, Vol. 45 Issue 8, p405 

    Discusses an isobaric-isothermal ensemble in statistical mechanics. Gibbs free-energy distribution; Modified constant pressure ensemble; Approximations to real physical systems.

  • Maximum Entropy Models for Quantum Systems. Łuczak, Andrzej; Podsędkowska, Hanna; Seweryn, Michał // Entropy;Jan2017, Vol. 19 Issue 1, p1 

    We show that for a finite von Neumann algebra, the states that maximise Segal's entropy with a given energy level are Gibbs states. This is a counterpart of the classical result for the algebra of all bounded linear operators on a Hilbert space and von Neumann entropy.

  • Current Reservoirs in the Simple Exclusion Process. Masi, A.; Presutti, E.; Tsagkarogiannis, D.; Vares, M. // Journal of Statistical Physics;Sep2011, Vol. 144 Issue 6, p1151 

    We consider the symmetric simple exclusion process in the interval [- N, N] with additional birth and death processes respectively on ( N- K, N], K>0, and [- N,- N+ K). The exclusion is speeded up by a factor N, births and deaths by a factor N. Assuming propagation of chaos (a property proved in...

  • Fluctuation theorem and chaos. Gallavottia, G. // European Physical Journal B -- Condensed Matter;Jul2008, Vol. 64 Issue 3/4, p315 

    The heat theorem (i.e. the second law of thermodynamics or the existence of entropy) is a manifestation of a general property of hamiltonian mechanics and of the ergodic hypothesis. In nonequilibrium thermodynamics of stationary states the chaotic hypothesis plays a similar role: it allows a...

  • An Entropy Measure of Non-Stationary Processes. Ling Feng Liu; Han Ping Hu; Ya Shuang Deng; Nai Da Ding // Entropy;Mar2014, Vol. 16 Issue 3, p1493 

    Shannon's source entropy formula is not appropriate to measure the uncertainty of non-stationary processes. In this paper, we propose a new entropy measure for non-stationary processes, which is greater than or equal to Shannon's source entropy. The maximum entropy of the non-stationary process...

  • Lattice Theoretic Aspects of Inference and Parameter Estimation. Lin, Juan K. // AIP Conference Proceedings;2005, Vol. 803 Issue 1, p310 

    We present a lattice representation of conditional probabilities defined on a set of random variables. We describe how information in the form of marginals and conditionals can be combined combinatorially, and show that the set of known conditionals consists of the union of order ideals on...

Share

Read the Article

Courtesy of NEW JERSEY STATE LIBRARY

Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics