Entropy, extropy and information potential in stochastic systems far from equilibrium

Gaveau, Bernard; Martinás, Katalin; Moreau, M.; Tóth, János

doi:10.1016/s0378-4371(01)00502-7

Cited by 13 publications

(8 citation statements)

References 37 publications

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“…The quantity −S(p 0 |p eq ) has been called the "extropy" of the distribution p 0 [4,11]: it is the total entropy production, or loss of information, when the system relaxes from p 0 to equilibrium when external constraints are suppressed. Since it is positive in non-equilibrium conditions, inequality (11) leaves the possibility of having positive work production in a non-equilibrium system, if the work necessary for creating or maintaining non-equilibrium is not taken into account.…”

Section: Constrained Non-equilibrium Systems Information Potentialmentioning

confidence: 99%

“…This is why we have recently started to develop another framework for non-equilibrium thermodynamics, based on the notion of coarse grained descriptions and of stochastic dynamics in the corresponding state space (see [2][3][4][5]). On the other hand, a different approach was introduced by Jarzynski [6], based on a Hamiltonian formalism, which was later widely discussed (see for instance [7][8][9][10] and references therein).…”

Section: Introductionmentioning

confidence: 99%

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Work and power production in non-equilibrium systems

2008

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Section: Constrained Non-equilibrium Systems Information Potentialmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Work and power production in non-equilibrium systems

2008

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“…For such a system, when the control parameter is held fixed, this free energy difference is a nonincreasing function of time. If the system is allowed to fully equilibrate, it is equal to the total entropy produced (also known as the extropy) [3]. Hence this free energy difference has also been called an entropy deficiency [4].…”

mentioning

confidence: 99%

Near-Equilibrium Measurements of Nonequilibrium Free Energy

Sivak

Crooks

2012

Phys. Rev. Lett.

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A central endeavor of thermodynamics is the measurement of free energy changes. Regrettably, although we can measure the free energy of a system in thermodynamic equilibrium, typically all we can say about the free energy of a nonequilibrium ensemble is that it is larger than that of the same system at equilibrium. Herein, we derive a formally exact expression for the probability distribution of a driven system, which involves path ensemble averages of the work over trajectories of the time-reversed system. From this we find a simple near-equilibrium approximation for the free energy in terms of an excess mean time-reversed work, which can be experimentally measured on real systems. With analysis and computer simulation, we demonstrate the accuracy of our approximations for several simple models.

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“…However, this binary information should be brought into correspondence with the measure of information expressed in thermodynamic terms. Here we should take into account that I M (in contrast to I S ) corresponds rather to the concept of extropy (the distance of a physical system from its equilibrium state on the entropic scale, i.e., the distance from the maximum of the entropy) [1], than to that of entropy, if one takes into account the thermodynamic analogies.…”

Section: Language Of Informationmentioning

confidence: 99%

On Symmetries and the Language of Information

Darvas

2011

Information

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Many writings on information mix information on a given system (IS), measurable information content of a given system (IM), and the (also measurable) information content that we communicate among us on a given system (IC). They belong to different levels and different aspects of information. The first (IS) involves everything that one possibly can, at least potentially, know about a system, but will never learn completely. The second (IM) contains quantitative data that one really learns about a system. The third (IC) relates rather to the language (including mathematical) by which we transmit information on the system to one another, rather than to the system itself. The information content of a system (IM —this is what we generally mean by information) may include all (relevant) data on each element of the system. However, we can reduce the quantity of information we need to mediate to each other (IC), if we refer to certain symmetry principles or natural laws which the elements of the given system correspond to. Instead of listing the data for all elements separately, even in a not very extreme case, we can give a short mathematical formula that informs about the data of the individual elements of the system. This abbreviated form of information delivery includes several conventions. These conventions are protocols that we have learnt before, and do not need to be repeated each time in the given community. These conventions include the knowledge that the scientific community accumulated earlier when discovered and formulated the symmetry principle or the law of nature, the language in which those regularities were discovered and formulated, for example, the symmetry principle or the law of nature, the language in which those regularities were formulated and then accepted by the community, and the mathematical marks and abbreviations that are known only for the members of the given scientific community. We do not need to repeat the rules of the convention each time, because the conveyed information includes them, and it is there in our minds behind our communicated data on the information content. I demonstrate this by using two examples, Kepler’s laws, and the law of correspondence between the DNA codons’ triplet structure and the individual amino acids which they encode. The information content of the language by which we communicate the obtained information cannot be identified with the information content of the system that we want to characterize, and moreover, it does not include all the possible information that we could potentially learn about the system. Symmetry principles and natural laws may reduce the information we need to communicate about a system, but we must keep in mind the conventions that we have learnt about the abbreviating mechanism of those principles, laws, and mathematical descriptions

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Entropy, extropy and information potential in stochastic systems far from equilibrium

Cited by 13 publications

References 37 publications

Work and power production in non-equilibrium systems

Work and power production in non-equilibrium systems

Near-Equilibrium Measurements of Nonequilibrium Free Energy

On Symmetries and the Language of Information

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