The Significance of Non-ergodic Property of Statistical Mechanics Systems for Understanding Resting State of a Living Cell (original) (raw)
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Journal of Statistical Physics, 1989
This is the first part of a series devoted to the study of thermodynamic behavior of large dynamical systems with the use of a family of fully-discrete and conservative models named elementary reversible cellular automata (ERCAs). In this paper, basic properties such as conservation laws and phase space structure are investigated in preparation for the later studies. ERCAs are a family of one-dimensional reversible cellular automata having two Boolean variables on each site. Reflection and Boolean conjugation symmetries divide them into 88 equivalence classes. For each rule, additive conserved quantities written in a certain form are regarded as a kind of energy, if they exist. By the aid of the discreteness of the variables, every ERCA satisfies the Liouville theorem or the preservation of phase space volume. Thus, if an energy exists in the above sense, statistical mechanics of the model can formally be constructed. If a locally defined quantity is conserved, however, it prevents the realization of statistical mechanics. The existence of such a quantity is examined for each class and a number of rules which have at least one energy but no local conservation laws are selected as hopeful candidates for the realization of thermodynamic behavior. In addition, the phase space structure of ERCAs is analyzed by enumerating cycles exactly in the phase space for systems of comparatively small sizes. As a result, it is revealed that a finite ERCA is not ergodic, that is, a large number of orbits coexist on an energy surface. It is argued that this fact does not necessarily mean the failure of thermodynamic behavior on the basis of an analogy with the ergodic nature of infinite systems.
Statistical thermodynamic theory of the cell cycle: the state variables of a collection of cells
Chemical Physics Letters, 2005
322] where a thermodynamic theory of the cell cycle has been introduced and the analogy with the kinetic theory has been discussed. Based on such conceptual framework, here we clarify the concept of metabolic temperature [A. Kummer, R. Ocone, Physica A 321 , we show how the latter is extended from a single cell to a collection of cells and we discuss the significance of thermodynamic-like variables such as pressure. In deriving the explicit form (the constitutive relation) for the metabolic pressure, we conclude that any other state variable for the cellular ÔensembleÕ can be derived from the theory.
Further Thoughts on Thermodynamics
viXra, 2016
Recently, attention has been drawn to a number of pieces written concerning classical thermodynamics in a biological setting. Several ideas have been put forward which are unusual for orthodox classical thermodynamics but, as they are supported by experiment, seem to offer suggestions for expanding the scope of that subject and even possibly helping make some aspects more amenable to students. The idea of introducing time into considerations is one such major notion which appears to lead to a new meaning of 'slow' processes in a classical thermodynamic setting and should be examined further because of the possible ramifications for the subject as a whole.
Biology and Thermodynamics: Seemingly-Opposite Phenomena in Search of a Unified Paradigm
It is probably not a coincidence that two of the pioneers of thermodynamics, Helmholtz and Mayer, were physicians. Thermodynamics studies the transformations of energy, and such transformations ceaselessly take place in all living systems (probably with important differences between the states of health and disease). Moreover, thermodynamics studies the elusive notions of order and disorder, which are also, respectively, the very hallmarks of life and death. These similarities suggest that thermodynamics might provide a unifying paradigm for many life sciences, explaining the multitude of life's manifestations on the basis of a few basic physical principles. In this article we introduce some basic thermodynamic concepts and point out their usefulness for the biologist and the physician. We hope to show that thermodynamics enables looking at the riddles of life from a new perspective and asking some new fruitful questions.
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.
Informational–statistical thermodynamics of a complex system
The Journal of Chemical Physics, 2000
We apply a statistical-thermodynamic approach to the study of a particular physical system ͑two sets of nonlinearly coupled oscillators͒, driven far away from equilibrium. Such a system displays a kind of complex behavior consisting in the so-called Fröhlich effect leading in steady-state conditions to a nonequilibrium phase condensation resembling the Bose-Einstein condensation of systems in equilibrium. A kind of ''two-fluid model'' arises: the ''normal nonequilibrium phase'' and Fröhlich condensate or ''nonequilibrium superphase,'' which is shown to be an attractor of the system. We work out some aspects of the irreversible thermodynamics of this dissipative complex system. Particular nonlinear properties are discussed and Lyapunov exponents determined. This kind of system gives a good modeling of polar vibration modes in polymers and biopolymers.
The Thermodynamics of the living organisms: entropy production in the cell
Trying to identify the entropy production within a cell has been part of debates and studies in the last century. First the idea was to make a resemblance of a cell with a Carnot engine, which is the most thermodynamically perfect machine. This approach was clearly not the best, since the yield achieved within a cell cannot be ideal, but can we even measure it? Several models approach the living cell, since the very simple one (e.g. Prigogine model) to more elaborated proposals. The concept of entropy has been the centre of discussions within several scientific fields. To interpret how entropy is produced in the complicated system of a cell is as hard as to understand how life originated at the first place. Understanding the way a cell works is key in biology, medicine, and multiple other scientific fields. Thermodynamics is essential in multitude of processes around us. Trying to identify the entropy production within a cell has been past of debates and studies in the last century....
New comments on "Possible divergences in Tsallis' thermostatistics
2014
}}), Plastino and Rocca suggest that the divergences inherent to the formulation of nonextensive statistical mechanics can be eliminated {\it {via}} the use of qqq-Laplace transformation which is illustrated for the case of a kinetic Hamiltonian system, the harmonic oscillator. The suggested new formulation raises questions which are discussed in the present comment.