Informational–statistical thermodynamics of a complex system (original) (raw)

Entropy, information theory, and the approach to equilibrium of coupled harmonic oscillator systems

Journal of Statistical Physics, 1969

Finite segments of infinite chains of classical coupled harmonic oscillators are treated as models of thermodynamic systems in contact with a heat bath, i.e., canonical ensembles. The Liouville function p for the infinite chain is reduced by integrating over the "outside" variables to a function pN of the variables of the N-particle segment that is the thermodynamic system. The reduced Liouville function pn, which is calculated from the dynamics of the infinite chain and the statistical knowledge of the coordinates and momenta at t = 0, is a time-dependent probability density in the 2N-dimensional phase space of the system. A Gibbs entropy defined in terms of pN measures the evolution of knowledge of the system (more accurately, the growth of missing pertinent information) in the sense of information theory. As p t [ -+ 0% energy is equipartitioned, the entropy evolves to the value expected from equilibrium statistical mechanics, and p~evolves to an equilibrium distribution function. The simple chain exhibits diffusion in coordinate space, i.e., Brownian motion, and the diffusivity is shown to depend only on the initial distribution of momenta (not of coordinates) in the heat bath. The harmonically bound chain, in the limit of weak coupling, serves as an excellent model for the approach to equilibrium of a canonical ensemble of weakly interacting particles.

Systems Biology: an information-theoretic-based thermo-statistical approach

Brazilian Journal of Physics, 2004

Systems Biology (system-level understanding in biological science), from the physical-chemical point of view, is involved with irreversible thermodynamics and nonlinear kinetic theory of open systems which are founded on nonequilibrium statistical mechanics. We describe a modern thermo-statistical approach for dealing with complex systems, in particular biological systems. We consider the case of a very peculiar complex behavior in open boson systems sufficiently away, from equilibrium, which appear to have large relevance in the functioning of biological systems. This is, on the one hand, the so-called Fröhlich-Bose-Einstein-like condensation leading in steady-state conditions to the emergence of a particular case of quantum-large-scale coherent ordering, of the type of a selforganizing-synergetic dissipative structure. Moreover, additional complexity emerges in the form of propagation, in this condensate, of signals (information) consisting of nearly undamped and undistorted, long-distance propagating, solitary waves (the pseudoparticle soliton). It can be accompanied by a so-called Fröhlich-Cherenkov cone of emission of polar vibrations, and it is also possible the formation of metastable states of the form of the so-called bioelectrets. These are phenomena apparently working in biological processes, which are presently gaining relevant status on the basis of eventually providing a large-scale quantum-coherent behavior in cytoskeletons of neurons and the conscious (non-computational) activity in the brain. Emphasis is centered on the quantum-mechanical-statistical irreversible thermodynamics of these open systems, and the informational characteristics of the phenomena. Ways for their experimental evidencing are pointed out and discussed.

Positive‐feedback‐enhanced Fröhlich's Bose–Einstein‐like condensation in biosystems

International Journal of Quantum Chemistry, 1998

We present a mechanostatistical study of the so-called Frohlich effect, namely nonthermal amplification of polar vibrations leading to complex behavior in biosystems, like biopolymers and large aggregates of macromolecules. Frohlicḧ condensation is considered to be of relevance for a certain class of biological processes, in particular in connection with the problem of long-range propagation of signals at physiological temperature. Resorting to a thermomechanical theory appropriate to deal with irreversible processes in systems far from equilibrium, earlier results are extended. We perform an analysis of the case when production of a double excitation of polar vibrations, generated by the action of an external pumping source of metabolic energy, is possible. It is shown that, when this is the case, the process involves a positive feedback mechanism that greatly facilitates and enhances the phenomenon of Frohlich's condensation, and consequently the possible accompanying biological processes. The results are discussed and eventual connection with experimental observations pointed out.

Statistical mechanical theory of an oscillating isolated system: The relaxation to equilibrium

Journal of Mathematical Physics, 2007

In this contribution we show that a suitably defined nonequilibrium entropy of an N-body isolated system is not a constant of the motion in general and its variation is bounded, the bounds determined by the thermodynamic entropy ,i.e. , the equilibrium entropy. We define the nonequilibrium entropy as a convex functional of the set of n-particle reduced distribution functions (n ≤ N ) generalizing the Gibbs fine-grained entropy formula. Additionally, as a consequence of our microscopic analysis we find that this nonequilibrium entropy behaves as a free entropic oscillator. In the approach to the equilibrium regime we find relaxation equations of the Fokker-Planck type, particularly for the one-particle distribution function.

Self-synchronization of populations of nonlinear oscillators in the thermodynamic limit

Journal of Statistical Physics, 1987

A population of identical nonlinear oscillators, subject to random forces and coupled via a mean-field interaction, is studied in the thermodynamic limit. The model presents a nonequilibrium phase transition from a stationary to a time-periodic probability density. Below the transition line, the population of oscillators is in a quiescent state with order parameter equal to zero. Above the transition line, there is a state of collective rhythmicity characterized by a time-periodic behavior of the order parameter and all moments of the probability distribution. The information entropy of the ensemble is a constant both below and above the critical line. Analytical and numerical analyses of the model are provided.

Nonequilibrium statistical mechanics of open classical systems

XIVth International Congress on Mathematical Physics, 2006

We describe the ergodic and thermodynamical properties of chains of anharmonic oscillators coupled, at the boundaries, to heat reservoirs at positive and different temperatures. We discuss existence and uniqueness of stationary states, rate of convergence to stationarity, heat flows and entropy production, Kubo formula and Gallavotti-Cohen fluctuation theorem.

Towards non-statistical foundation of thermodynamics

IOP Conference Series: Materials Science and Engineering, 2018

It is shown that the irreversible behavior exists even in two-body system. It is due to the retardation of the interactions between the particles. It is established that a two-particle oscillator with a delayed interaction between particles has an infinite spectrum of both stationary and nonstationary oscillations, which depends on the equilibrium distance between the particles.

Links between nonlinear dynamics and statistical mechanics in a simple one-dimensional model

2004

We consider the links between nonlinear dynamics and thermodynamics in the framework of a simple nonlinear model for DNA. Two analyses of the phase transition, either with the transfer integral approach or by considering the instability of a nonlinear particular solution, are discussed. Conversely, the computation of the largest Lyapunov exponent is obtained within a thermodynamic treatment. Differences with the Peyrard-Bishop model are also discussed.

Origins and diagnostics of the nonequilibrium character of active systems

Journal of Statistical Mechanics: Theory and Experiment

We present in detail a Langevin formalism for constructing stochastic dynamical equations for active-matter systems coupled to a thermal bath. We apply the formalism to clarify issues of principle regarding the sources and signatures of nonequilibrium behaviour in a variety of polar and apolar single-particle systems and polar flocks. We show that distance from thermal equilibrium depends on how time-reversal is implemented and hence on the reference equilibrium state. We predict characteristic forms for the frequencyresolved entropy production for an active polar particle in a harmonic potential, which should be testable in experiments.

Oscillatory Shannon entropy in the process of equilibration of nonequilibrium crystalline systems

Chinese Physics B, 2015

PACS 89.70.Cf-Entropy and other measures of information PACS 65.40.gd-Entropy in condensed matter PACS 05.70.Ln-Nonequilibrium and irreversible thermodynamics Abstract-We present a study of the equilibration process of nonequilibrium systems by means of molecular dynamics simulation technique. The nonequilibrium conditions are achieved in systems by defining velocity components of the constituent atoms randomly. The calculated Shannon entropy from the probability distribution of the kinetic energy among the atoms at different instants during the process of equilibration shows oscillation as the system relaxes towards equilibrium. Fourier transformations of these oscillating Shannon entropies reveal the existance of Debye frequency of the concerned system. From these studies it was concluded that the signature of the equilibration process of dynamical systems is the time invariance of Shannon entropy.