Senin, 09 Maret 2015

Thermodynamics

Thermodynamics

Thermodynamics is a branch of physics that studies the movement of energy and how energy instills movement. More precisely, it studies the effects of changes in temperature, pressure, and volume on physical systems at the macroscopic scale by analyzing the collective motion of their particles using statistics. 19th century physicists defined three Laws of thermodynamics to sum up the basic principles of the subject; in the 20th century, an unofficial "zeroth law" was added.

Sourced[edit]

  • Every mathematician knows it is impossible to understand an elementary course in thermodynamics.
    • V.I. Arnold, "Contact geometry: The geometrical method of Gibbs' thermodynamics," in Proceedings of the Gibbs Symposium, D. Caldi and G. Mostow, eds. (American Mathematical Society, 1990), p. 163.
  • ̈Machines which do not receive their motion from heat... can be studied even to their smallest details by the mechanical theory. ...A similar theory is evidently needed for heat-engines. We shall have it only when the laws of Physics shall be extended enough, generalized enough, to make known beforehand all of the effects of heat acting in a determined manner on any body.
    • Nicolas Léonard Sadi Carnot, Reflections on the Motive Power of Heat and on Machines Fitted to Develop Power(1824)
  • The production of heat alone is not sufficient to give birth to the impelling powerː it is necessary that there should also be cold; without it the heat would be useless. And in fact, if we should find about us only bodies as hot as our furnaces... What should we do with it if once produced? We should not presume that we might discharge it into the atmosphere... the atmosphere would not receive it. It does receive it under the actual condition of things only because.. it is at a lower temperature, otherwise it... would be already saturated.
    • Nicolas Léonard Sadi Carnot, Reflections on the Motive Power of Heat and on Machines Fitted to Develop Power(1824)
  • Heat can evidently be a cause of motion only by virtue of the changes of volume or of form which it produces in bodies. These changes are not caused by uniform temperature but rather by alternations of heat and cold.

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Does the Universe Violate the Laws of Thermodynamics

Does the Universe Violate the Laws of Thermodynamics?

Total energy must be conserved. Every student of physics learns this fundamental law. The trouble is, it does not apply to the universe as a whole
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Mark Hooper
Energy can neither be created nor destroyed. This principle, called conservation of energy, is one of our most cherished laws of physics. It governs every part of our lives: the heat it takes to warm up a cup of coffee; the chemical reactions that produce oxygen in the leaves of trees; the orbit of Earth around the sun; the food we need to keep our hearts beating. We cannot live without eating, cars do not run without fuel, and perpetual-motion machines are just a mirage. So when an experiment seems to violate the law of energy conservation, we are rightfully suspicious. What happens when our observations seem to contradict one of science's most deeply held notions: that energy is always conserved?
Skip for a moment outside our Earthly sphere and consider the wider universe. Almost all of our information about outer space comes in the form of light, and one of light's key features is that it gets redshifted—its electromagnetic waves get stretched—as it travels from distant galaxies through our ever expanding universe, in accordance with Albert Einstein's general theory of relativity. But the longer the wavelength, the lower the energy. Thus, inquisitive minds ask: When light is redshifted by the expansion of the universe, where does its energy go? Is it lost, in violation of the conservation principle?

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Physics Study Guide/Thermodynamics

Physics Study Guide/Thermodynamics


Introduction[edit]

Thermodynamics deals with the movement of heat and its conversion to mechanical and electrical energy among others.

Laws of Thermodynamics[edit]

First Law[edit]

The First Law is a statement of conservation of energy law:

\Delta U = Q - W
The First Law can be expressed as the change in internal energy of a system (\Delta U) equals the amount of energy added to a system (Q), such as heat, minus the work expended by the system on its surroundings (W).
If Q is positive, the system has gained energy (by heating).
If W is positive, the system has lost energy from doing work on its surroundings.
As written the equations have a problem in that neither Q or W are state functions or quantities which can be known by direct measurement without knowing the history of the system.
In a gas, the first law can be written in terms of state functions as

dU = T ds - p dV

Zero-th Law[edit]

After the first law of Thermodynamics had been named, physicists realised that there was another more fundamental law, which they termed the 'zero-th'.
This is that:

If two bodies are at the same temperature, there is no resultant heat flow between them.
An alternate form of the 'zero-th' law can be described:

If two bodies are in thermal equilibrium with a third, all are in thermal equilibrium with each other.
This second statement, in turn, gives rise to a definition of Temperature (T):

Temperature is the only thing that is the same between two otherwise unlike bodies that are in thermal equilibrium with each other.

Second Law[edit]

This law states that heat will never of itself flow from a cold object to a hot object.

S = k_B \cdot ln(\Omega)
where k_B is the Boltzmann constant (k_B = 1.380658 \cdot 10^{-23}  \mbox{ kg m}^2 \mbox{ s}^{-2} \mbox{ K}^{-1}) and \Omega is the partition function, i. e. the number of all possible states in the system.
This was the statistical definition of entropy, there is also a "macroscopic" definition:

S = \int  \frac{\mathrm{d}Q}{T}
where T is the temperature and dQ is the increment in energy of the system.

Third Law[edit]

The third law states that a temperature of absolute zero cannot be reached.

Temperature Scales[edit]


There are several different scales used to measure temperature. Those you will most often come across in physics are degrees Celsius and kelvins.
Celsius temperatures use the symbol Θ. The symbol for degrees Celsius is °C. Kelvin temperatures use the symbol T. The symbol for kelvins is K.


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Second Law-Like Inequalities with Quantum Relative Entropy: An Introduction

Second Law-Like Inequalities with Quantum Relative Entropy: An Introduction

 Takahiro Sagawa ∗†‡ February 25, 2014 

Abstract 
We review the fundamental properties of the quantum relative entropy for finite-dimensional Hilbert spaces. In particular, we focus on several inequalities that are related to the second law of thermodynamics, where the positivity and the monotonicity of the quantum relative entropy play key roles; these properties are directly applicable to derivations of the second law (e.g., the Clausius inequality). Moreover, the positivity is closely related to the quantum fluctuation theorem, while the monotonicity leads to a quantum version of the Hatano-Sasa inequality for nonequilibrium steady states. On the basis of the monotonicity, we also discuss the data processing inequality for the quantum mutual information, which has a similar mathematical structure to that of the second law. Moreover, we derive a generalized second law with quantum feedback control. In addition, we review a proof of the monotonicity in line with Petz [108]. 


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Geometrical Expression of Excess Entropy Production

Geometrical Expression of Excess Entropy Production 

Takahiro Sagawa1,2 and Hisao Hayakawa2 1The Hakubi Center, The Kyoto University, Yoshida-Ushinomiya-cho, Sakyo-ku, Kyoto 606-8302, Japan 2Yukawa Institute for Theoretical Physics, The Kyoto University, Kitashirakawa Oiwake-Cho, 606-8502 Kyoto, Japan (Dated: November 17, 2011) 

We derive a geometrical expression of the excess entropy production for quasi-static transitions between nonequilibrium steady states of Markovian jump processes, which can be exactly applied to nonlinear and nonequilibrium situations. The obtained expression is geometrical; the excess entropy production depends only on a trajectory in the parameter space, analogous to the Berry phase in quantum mechanics. Our results imply that vector potentials are needed to construct the thermodynamics of nonequilibrium steady states.

PACS numbers: 05.70.Ln, 05.40.-a, 02.50.Ga


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http://arxiv.org/pdf/1109.0796.pdf

Thermodynamics of Information Processing in Small Systems˜)

INVITED PAPERS

 1 Progress of Theoretical Physics, Vol. 127, No. 1, January 2012

Thermodynamics of Information Processing in Small Systems˜) 

Takahiro Sagawa1,2 1The Hakubi Center, Kyoto University, Kyoto 606-8302, Japan 2Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan (Received October 24, 2011) 

We review a general theory of thermodynamics of information processing. The background of this topic is the recently-developed nonequilibrium statistical mechanics and quantum (and classical) information theory. These theories are closely related to the modern technologies to manipulate and observe small systems; for example, macromolecules and colloidal particles in the classical regime, and quantum-optical systems and quantum dots in the quantum regime. First, we review a generalization of the second law of thermodynamics to the situations in which small thermodynamic systems are subject to quantum feedback control. The generalized second law is expressed in terms of an inequality that includes the term of information obtained by the measurement, as well as the thermodynamic quantities such as the free energy. This inequality leads to the fundamental upper bound of the work that can be extracted by a “Maxwell’s demon”, which can be regarded as a feedback controller with a memory that stores measurement outcomes. Second, we review generalizations of the second law of thermodynamics to the measurement and information erasure processes of the memory of the demon that is a quantum system. The generalized second laws consist of inequalities that identify the lower bounds of the energy costs that are needed for the measurement and the information erasure. The inequality for the erasure leads to the celebrated Landauer’s principle for a special case. Moreover, these inequalities enable us to reconcile Maxwell’s demon with the second law of thermodynamics. In these inequalities, thermodynamic quantities and information contents are treated on an equal footing. In fact, the inequalities are model-independent, so that they can be applied to a broad class of information processing. Therefore, these inequalities can be called the second law of “information thermodynamics”.
Subject Index: 058


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http://ptp.oxfordjournals.org/content/127/1/1.full.pdf

Information Thermodynamics on Causal Networks

Information Thermodynamics on Causal Networks

 Sosuke Ito1 and Takahiro Sagawa2 1Department of Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan 2Department of Basic Science, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8902, Japan (Dated: November 7, 2013)

 We study nonequilibrium thermodynamics of complex information flows induced by interactions between multiple fluctuating systems. Characterizing nonequilibrium dynamics by causal networks (i.e., Bayesian networks), we obtain novel generalizations of the second law of thermodynamics and the fluctuation theorem, which include an informational quantity characterized by the topology of the causal network. Our result implies that the entropy production in a single system in the presence of multiple other systems is bounded by the information flow between these systems. We demonstrate our general result by a simple model of biochemical adaptation.

PACS numbers: 05.20.-y, 05.40.Jc, 05.70.Ln, 89.70.-a

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http://arxiv.org/pdf/1306.2756.pdf

conversion and validation of the generalized Jarzynski equality

Experimental demonstration of information-to-energy conversion and validation of the generalized Jarzynski equality

Nature Physics
 
6,
 
988–992
 
 
doi:10.1038/nphys1821
Received
 
Accepted
 
Published online
 
In 1929, Leó Szilárd invented a feedback protocol1 in which a hypothetical intelligence—dubbed Maxwell’s demon—pumps heat from an isothermal environment and transforms it into work. After a long-lasting and intense controversy it was finally clarified that the demon’s role does not contradict the second law of thermodynamics, implying that we can, in principle, convert information to free energy23456. An experimental demonstration of this information-to-energy conversion, however, has been elusive. Here we demonstrate that a non-equilibrium feedback manipulation of a Brownian particle on the basis of information about its location achieves a Szilárd-type information-to-energy conversion. Using real-time feedback control, the particle is made to climb up a spiral-staircase-like potential exerted by an electric field and gains free energy larger than the amount of work done on it. This enables us to verify the generalized Jarzynski equality7, and suggests a new fundamental principle of an ‘information-to-heat engine’ that converts information into energy by feedback control.
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Second Law of Thermodynamics with Discrete Quantum Feedback Control

Second Law of Thermodynamics with Discrete Quantum Feedback Control 

Takahiro Sagawa1 and Masahito Ueda1,2 1Department of Physics, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551, Japan 2ERATO Macroscopic Quantum Control Project, JST, 2-11-16 Yayoi, Bunkyo-ku, Tokyo 113-8656, Japan (Dated: February 28, 2008) 


A new thermodynamic inequality is derived which leads to the maximum work that can be extracted from multi-heat baths with the assistance of discrete quantum feedback control. The maximum work is determined by the free-energy difference and a generalized mutual information content between the thermodynamic system and the feedback controller. This maximum work can exceed that in conventional thermodynamics and, in the case of a heat cycle with two heat baths, the heat efficiency can be greater than that of the Carnot cycle. The consistency of our results with the second law of thermodynamics is ensured by the fact that work is needed for information processing of the feedback controller. PACS numbers: 03.67.-a,05.70.Ln,05.30.-d,03.65.Ta

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Phase Transitions, Geometrothermodynamics, and Critical Exponents of Black Holes with Conformal Anomaly

Advances in High Energy Physics
Volume 2014 (2014), Article ID 739454, 10 pages
http://dx.doi.org/10.1155/2014/739454
Research Article

Phase Transitions, Geometrothermodynamics, and Critical Exponents of Black Holes with Conformal Anomaly

1Department of Physics, Institute of Theoretical Physics, Beijing Normal University, Beijing 100875, China
2Institute of Theoretical Physics, Zhanjiang Normal University, Zhanjiang 524048, China
Received 9 December 2013; Accepted 3 February 2014; Published 13 March 2014
Academic Editor: George Siopsis
Copyright © 2014 Jie-Xiong Mo and Wen-Biao Liu. This is an open access article distributed under theCreative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP3.

Linked References

  1. J. D. Bekenstein, “Black holes and entropy,” Physical Review D, vol. 7, no. 8, pp. 2333–2346, 1973.View at Publisher · View at Google Scholar · View at Scopus
  2. S. W. Hawking, “Particle creation by black holes,” Communications in Mathematical Physics, vol. 43, p. 199, 1975.
  3. S. W. Hawking and D. N. Page, “Thermodynamics of black holes in anti-de Sitter space,”Communications in Mathematical Physics, vol. 87, no. 4, pp. 577–588, 1983. View at Publisher · View at Google Scholar · View at Scopus
  4. J. Maldacena, “The large N Limit of superconformal field theories and supergravity,” Advances in Theoretical and Mathematical Physics, vol. 2, no. 2, pp. 231–252, 1998. View at Scopus

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History of physics

History of physics

From Wikipedia, the free encyclopedia
"If I have seen further, it is only by standing on the shoulders of giants." – Isaac Newton[1]
Physics (from the Ancient Greek φύσις physis meaning "nature") is the fundamental branch of science that developed out of the study of nature and philosophy known, until around the end of the 19th century, as "natural philosophy". Today, physics is ultimately defined as the study of matterenergy and the relationships between them.[citation needed] Physics is, in some senses, the oldest and most basic pure science; its discoveries find applications throughout the natural sciences, since matter and energy are the basic constituents of the natural world. The other sciences are generally more limited in their scope and may be considered branches that have split off from physics to become sciences in their own right. Physics today may be divided loosely into classical physics and modern physics.

Ancient history[edit]

Further information: History of astronomy
Elements of what became physics were drawn primarily from the fields of astronomyoptics, and mechanics, which were methodologically united through the study of geometry. These mathematical disciplines began in antiquity with theBabylonians and with Hellenistic writers such as Archimedes and PtolemyAncient philosophy, meanwhile – including what was called "physics" – focused on explaining nature through ideas such as Aristotle's four types of "cause".

Ancient Greece[edit]

The move towards a rational understanding of nature began at least since the Archaic period in Greece (650–480 BCE) with the Pre-Socratic philosophers. The philosopher Thales of Miletus (7th and 6th centuries BCE), dubbed "the Father of Science" for refusing to accept various supernatural, religious or mythological explanations for natural phenomena, proclaimed that every event had a natural cause.[2] Thales also made advancements in 580 BCE by suggesting that water is the basic element, experimenting with the attraction between magnets and rubbed amber and formulating the first recorded cosmologiesAnaximander, famous for his proto-evolutionary theory, disputed the Thales' ideas and proposed that rather than water, a substance called apeiron was the building block of all matter. Around 500 BCE, Heraclitusproposed that the only basic law governing the Universe was the principle of change and that nothing remains in the same state indefinitely. This observation made him one of the first scholars in ancient physics to address the role of time in the universe, a key and sometimes contentious concept in modern and present-day physics.[citation needed] The early physicistLeucippus (fl. first half of the 5th century BCE) adamantly opposed the idea of direct divine intervention in the universe, proposing instead that natural phenomena had a natural cause. Leucippus and his student Democritus were the first to develop the theory of atomism, the idea that everything is composed entirely of various imperishable, indivisible elements called atoms.
Aristotle
(384–322 BCE)
During the classical period in Greece (6th, 5th and 4th centuries BCE) and in Hellenistic timesnatural philosophy slowly developed into an exciting and contentious field of study.Aristotle (GreekἈριστοτέληςAristotélēs) (384 – 322 BCE), a student of Plato, promoted the concept that observation of physical phenomena could ultimately lead to the discovery of the natural laws governing them. Aristotle's writings cover physics, metaphysicspoetry,theatermusiclogicrhetoriclinguisticspoliticsgovernmentethicsbiology and zoology. He wrote the first work which refers to that line of study as "Physics" – in the 4th century BCE, Aristotle founded the system known as Aristotelian physics. He attempted to explain ideas such as motion (and gravity) with the theory of four elements. Aristotle believed that all matter was made up of aether, or some combination of four elements: earth, water, air, and fire. According to Aristotle, these four terrestrial elements are capable of inter-transformation and move toward their natural place, so a stone falls downward toward the center of the cosmos, but flames rise upward toward the circumference. Eventually,Aristotelian physics became enormously popular for many centuries in Europe, informing the scientific and scholastic developments of the Middle Ages. It remained the mainstream scientific paradigm in Europe until the time of Galileo Galilei and Isaac Newton.
Early in Classical Greece, knowledge that the Earth is spherical ("round") was common. Around 240 BCE, as the result a seminal experimentEratosthenes (276–194 BCE) accurately estimated its circumference. In contrast to Aristotle's geocentric views, Aristarchus of Samos (GreekἈρίσταρχος; c.310 – c.230 BCE) presented an explicit argument for aheliocentric model of the Solar system, i.e. for placing the Sun, not the Earth, at its centre. Seleucus of Seleucia, a follower of Aristarchus' heliocentric theory, stated that the Earth rotated around its own axis, which, in turn, revolved around the Sun. Though the arguments he used were lost, Plutarch stated that Seleucus was the first to prove the heliocentric system through reasoning.
The ancient Greek mathematicianArchimedes, famous for his ideas regarding fluid mechanics andbuoyancy.
In the 3rd century BCE, the Greek mathematician Archimedes of Syracuse (Greek:Ἀρχιμήδης (287–212 BCE) – generally considered to be the greatest mathematician of antiquity and one of the greatest of all time – laid the foundations of hydrostatics,statics and calculated the underlying mathematics of the lever. A leading scientist of classical antiquity, Archimedes also developed elaborate systems of pulleys to move large objects with a minimum of effort. The Archimedes' screw underpins modern hydroengineering, and his machines of war helped to hold back the armies of Rome in the First Punic War. Archimedes even tore apart the arguments of Aristotle and his metaphysics, pointing out that it was impossible to separate mathematics and nature and proved it by converting mathematical theories into practical inventions. Furthermore, in his work On Floating Bodies, around 250 BCE, Archimedes developed the law of buoyancy, also known as Archimedes' Principle. In mathematics, Archimedes used the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series, and gave a remarkably accurate approximation of pi. He also defined the spiral bearing his name, formulae for the volumes of surfaces of revolution and an ingenious system for expressing very large numbers. He also developed the principles of equilibrium states and centers of gravity, ideas that would influence the Islamic scholars, Galileo, and Newton.
Hipparchus (190–120 BCE), focusing on astronomy and mathematics, used sophisticated geometrical techniques to map the motion of the stars and planets, even predicting the times that Solar eclipses would happen. In addition, he added calculations of the distance of the Sun and Moon from the Earth, based upon his improvements to the observational instruments used at that time. Another of the most famous of the early physicists was Ptolemy (90–168 CE), one of the leading minds during the time of the Roman Empire. Ptolemy was the author of several scientific treatises, at least three of which were of continuing importance to later Islamic and European science. The first is the astronomical treatise now known as the Almagest (in Greek, Ἡ Μεγάλη Σύνταξις, "The Great Treatise", originally Μαθηματικὴ Σύνταξις, "Mathematical Treatise"). The second is the Geography, which is a thorough discussion of the geographic knowledge of the Greco-Roman world.
Much of the accumulated knowledge of the ancient world was lost. Even of the works of the better known thinkers, few fragments survived. Although he wrote at least fourteen books, almost nothing of Hipparchus' direct work survived. Of the 150 reputed Aristotelian works, only 30 exist, and some of those are "little more than lecture notes".

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