Demon algorithm - Revision history

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2024-06-07T15:16:02Z

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		⚫	{{no footnotes\|date=January 2011}}
	The '''demon algorithm''' is a [[Monte Carlo method]] for efficiently sampling members of a [[microcanonical ensemble]] with a given energy. An additional degree of freedom, called 'the demon', is added to the system and is able to store and provide energy. If a drawn microscopic state has lower energy than the original state, the excess energy is transferred to the demon. For a sampled state that has higher energy than desired, the demon provides the missing energy if it is available. The demon can not have negative energy and it does not interact with the particles beyond exchanging energy. Note that the additional degree of freedom of the demon does not alter a system with many particles significantly on a macroscopic level.		The '''demon algorithm''' is a [[Monte Carlo method]] for efficiently sampling members of a [[microcanonical ensemble]] with a given energy. An additional degree of freedom, called 'the demon', is added to the system and is able to store and provide energy. If a drawn microscopic state has lower energy than the original state, the excess energy is transferred to the demon. For a sampled state that has higher energy than desired, the demon provides the missing energy if it is available. The demon can not have negative energy and it does not interact with the particles beyond exchanging energy. Note that the additional degree of freedom of the demon does not alter a system with many particles significantly on a macroscopic level.

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	* [[Monte Carlo methods]]		* [[Monte Carlo methods]]
	* [[Metropolis algorithm]] to sample microscopic states at a fixed temperature		* [[Metropolis algorithm]] to sample microscopic states at a fixed temperature

⚫	{{no footnotes\|date=January 2011}}

	== References ==		== References ==

Citation bot: Altered title. Added edition. | Use this bot. Report bugs. | Suggested by Eastmain | #UCB_webform 3/102

2024-02-01T04:34:07Z

Altered title. Added edition. | Use this bot. Report bugs. | Suggested by Eastmain | #UCB_webform 3/102

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	* {{cite book		* {{cite book
	\| author = Harvey Gould and Jan Tobochnik and Wolfgang Christian		\| author = Harvey Gould and Jan Tobochnik and Wolfgang Christian
	\| title = An Introduction to Computer Simulation Methods: Applications to Physical Systems ~~(3rd Edition)~~		\| title = An Introduction to Computer Simulation Methods: Applications to Physical Systems
	\| publisher = Addison Wesley		\| publisher = Addison Wesley
	\| year = 2006		\| year = 2006
	\| isbn = 978-0-8053-7758-3		\| isbn = 978-0-8053-7758-3
	\| chapter= Chapter 15: Monte Carlo Simulations of Thermal Systems		\| chapter= Chapter 15: Monte Carlo Simulations of Thermal Systems
			\| edition = 3rd
	}}		}}
	* {{cite journal		* {{cite journal

42.106.28.105 at 13:36, 15 September 2021

2021-09-15T13:36:18Z

← Previous revision		Revision as of 13:36, 15 September 2021
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	The '''demon algorithm''' is a [[Monte Carlo method]] for efficiently sampling members of a [[microcanonical ensemble]] with a given energy. An additional degree of freedom, called 'the demon', is added to the system and is able to store and provide energy. If a drawn microscopic state has lower energy than the original state, the excess energy is transferred to the demon. For a sampled state that has higher energy than desired, the demon provides the missing energy if it is available. The demon can not have negative energy and it does not interact with the particles beyond exchanging energy. Note that the additional degree of freedom of the demon does not alter a system with many particles significantly on a macroscopic level.		The '''demon algorithm''' is a [[Monte Carlo method]] for efficiently sampling members of a [[microcanonical ensemble]] with a given energy. An additional degree of freedom, called 'the demon', is added to the system and is able to store and provide energy. If a drawn microscopic state has lower energy than the original state, the excess energy is transferred to the demon. For a sampled state that has higher energy than desired, the demon provides the missing energy if it is available. The demon can not have negative energy and it does not interact with the particles beyond exchanging energy. Note that the additional degree of freedom of the demon does not alter a system with many particles significantly on a macroscopic level.

	== Motivation ==
	In [[thermodynamical system]]s, equal macroscopic properties (e. g. temperature) can result from different microscopic properties (e. g. velocities of individual particles). Computer simulations of the full equations of motion for every individual particle to simulate microscopic properties is computationally very expensive. [[Monte Carlo methods]] can overcome this problem by sampling microscopic states according to stochastic rules instead of modeling the complete microphysics.		In [[thermodynamical system]]s, equal macroscopic properties (e. g. temperature) can result from different microscopic properties (e. g. velocities of individual particles). Computer simulations of the full equations of motion for every individual particle to simulate microscopic properties is computationally very expensive. [[Monte Carlo methods]] can overcome this problem by sampling microscopic states according to stochastic rules instead of modeling the complete microphysics.

Frap: /* The demon algorithm */ semantic list

2019-12-17T15:45:04Z

The demon algorithm: semantic list

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	The full procedure can be summarized by the following steps:		The full procedure can be summarized by the following steps:

	1. Perform a random change in the state of a randomly chosen particle (e. g. change velocity or position).		# Perform a random change in the state of a randomly chosen particle (e. g. change velocity or position).
			# Calculate the change in energy <math>\Delta E</math> of the thermal system.

	2. ~~Calculate~~ the ~~change~~ in ~~energy~~ <math>\Delta E</math> of the ~~thermal~~ ~~system~~.		# Negative <math>\Delta E</math>, i. e. excess energy, is given to the demon by adding <math>\|\Delta E\|</math> to the demon. This case (<math>\Delta E < 0</math>) is always accepted.
		⚫	# The demon provides positive <math>\Delta E</math> to keep the total energy constant only if it has sufficient energy, i. e. <math>E_d > \Delta E</math>. In this case the change is accepted, otherwise the randomly chosen change in velocity is rejected and the algorithm is restarted from the original microscopic state.

		⚫	# If the change is accepted, repeat the algorithm for the new configuration.
	3. Negative <math>\Delta E</math>, i. e. excess energy, is given to the demon by adding <math>\|\Delta E\|</math> to the demon. This case (<math>\Delta E < 0</math>) is always accepted.

⚫	4. The demon provides positive <math>\Delta E</math> to keep the total energy constant only if it has sufficient energy, i. e. <math>E_d > \Delta E</math>. In this case the change is accepted, otherwise the randomly chosen change in velocity is rejected and the algorithm is restarted from the original microscopic state.

⚫	5. If the change is accepted, repeat the algorithm for the new configuration.

	Since energy fluctuations per degree of freedom are only of order 1/''N'', the presence of the demon has little effect on macroscopic properties of systems with high numbers of particles. After many iterations of the algorithm, the interplay of demon and random energy changes equilibrates the system. Assuming that a particular system approaches all possible states over very long times ([[ergodic theory\|quasi-ergodicity]]), the resulting Monte Carlo dynamics realistically sample microscopic states that correspond to the given energy value. This is only true if macroscopic quantities are stable over many Monte Carlo steps, i. e. if the system is at equilibrium.		Since energy fluctuations per degree of freedom are only of order 1/''N'', the presence of the demon has little effect on macroscopic properties of systems with high numbers of particles. After many iterations of the algorithm, the interplay of demon and random energy changes equilibrates the system. Assuming that a particular system approaches all possible states over very long times ([[ergodic theory\|quasi-ergodicity]]), the resulting Monte Carlo dynamics realistically sample microscopic states that correspond to the given energy value. This is only true if macroscopic quantities are stable over many Monte Carlo steps, i. e. if the system is at equilibrium.

Monkbot: /* References */Fix CS1 deprecated date parameter errors

2014-01-16T14:45:54Z

References: Fix CS1 deprecated date parameter errors

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	\| issue = 19		\| issue = 19
	\| pages = 1411–1414		\| pages = 1411–1414
	\| ~~year~~ = 1983		\|date=May 1983
	\| month = May
	\| doi = 10.1103/PhysRevLett.50.1411		\| doi = 10.1103/PhysRevLett.50.1411
	\| publisher = American Physical Society		\| publisher = American Physical Society

MaxwellDecoherence: /* The demon algorithm */ equilibriate > equilibrate

2012-07-30T20:18:56Z

The demon algorithm: equilibriate > equilibrate

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	5. If the change is accepted, repeat the algorithm for the new configuration.		5. If the change is accepted, repeat the algorithm for the new configuration.

	Since energy fluctuations per degree of freedom are only of order 1/''N'', the presence of the demon has little effect on macroscopic properties of systems with high numbers of particles. After many iterations of the algorithm, the interplay of demon and random energy changes ~~equilibriates~~ the system. Assuming that a particular system approaches all possible states over very long times ([[ergodic theory\|quasi-ergodicity]]), the resulting Monte Carlo dynamics realistically sample microscopic states that correspond to the given energy value. This is only true if macroscopic quantities are stable over many Monte Carlo steps, i. e. if the system is at equilibrium.		Since energy fluctuations per degree of freedom are only of order 1/''N'', the presence of the demon has little effect on macroscopic properties of systems with high numbers of particles. After many iterations of the algorithm, the interplay of demon and random energy changes equilibrates the system. Assuming that a particular system approaches all possible states over very long times ([[ergodic theory\|quasi-ergodicity]]), the resulting Monte Carlo dynamics realistically sample microscopic states that correspond to the given energy value. This is only true if macroscopic quantities are stable over many Monte Carlo steps, i. e. if the system is at equilibrium.

	== See also ==		== See also ==

Helpful Pixie Bot: ISBNs (Build KC)

2012-05-05T23:45:26Z

ISBNs (Build KC)

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	\| publisher = Addison Wesley		\| publisher = Addison Wesley
	\| year = 2006		\| year = 2006
	\| isbn = ~~9780805377583~~		\| isbn = 978-0-8053-7758-3
	\| chapter= Chapter 15: Monte Carlo Simulations of Thermal Systems		\| chapter= Chapter 15: Monte Carlo Simulations of Thermal Systems
	}}		}}

213.103.219.248: added linl

2012-03-25T11:08:29Z

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← Previous revision		Revision as of 11:08, 25 March 2012
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	The '''demon algorithm''' is a [[Monte Carlo method]] for efficiently sampling members of a microcanonical ensemble with a given energy. An additional degree of freedom, called 'the demon', is added to the system and is able to store and provide energy. If a drawn microscopic state has lower energy than the original state, the excess energy is transferred to the demon. For a sampled state that has higher energy than desired, the demon provides the missing energy if it is available. The demon can not have negative energy and it does not interact with the particles beyond exchanging energy. Note that the additional degree of freedom of the demon does not alter a system with many particles significantly on a macroscopic level.		The '''demon algorithm''' is a [[Monte Carlo method]] for efficiently sampling members of a [[microcanonical ensemble]] with a given energy. An additional degree of freedom, called 'the demon', is added to the system and is able to store and provide energy. If a drawn microscopic state has lower energy than the original state, the excess energy is transferred to the demon. For a sampled state that has higher energy than desired, the demon provides the missing energy if it is available. The demon can not have negative energy and it does not interact with the particles beyond exchanging energy. Note that the additional degree of freedom of the demon does not alter a system with many particles significantly on a macroscopic level.

	== Motivation ==		== Motivation ==

Vice regent at 06:04, 13 December 2011

2011-12-13T06:04:27Z

← Previous revision		Revision as of 06:04, 13 December 2011
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	The demon algorithm is a Monte Carlo method for efficiently sampling members of a microcanonical ensemble with a given energy. An additional degree of freedom, called 'the demon', is added to the system and is able to store and provide energy. If a drawn microscopic state has lower energy than the original state, the excess energy is transferred to the demon. For a sampled state that has higher energy than desired, the demon provides the missing energy if it is available. The demon can not have negative energy and it does not interact with the particles beyond exchanging energy. Note that the additional degree of freedom of the demon does not alter a system with many particles significantly on a macroscopic level.		The '''demon algorithm''' is a [[Monte Carlo method]] for efficiently sampling members of a microcanonical ensemble with a given energy. An additional degree of freedom, called 'the demon', is added to the system and is able to store and provide energy. If a drawn microscopic state has lower energy than the original state, the excess energy is transferred to the demon. For a sampled state that has higher energy than desired, the demon provides the missing energy if it is available. The demon can not have negative energy and it does not interact with the particles beyond exchanging energy. Note that the additional degree of freedom of the demon does not alter a system with many particles significantly on a macroscopic level.

	== Motivation ==		== Motivation ==

Frozenport: Quick fix

2011-09-23T09:06:23Z

Quick fix

← Previous revision		Revision as of 09:06, 23 September 2011
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		⚫	The demon algorithm is a Monte Carlo method for efficiently sampling members of a microcanonical ensemble with a given energy. An additional degree of freedom, called 'the demon', is added to the system and is able to store and provide energy. If a drawn microscopic state has lower energy than the original state, the excess energy is transferred to the demon. For a sampled state that has higher energy than desired, the demon provides the missing energy if it is available. The demon can not have negative energy and it does not interact with the particles beyond exchanging energy. Note that the additional degree of freedom of the demon does not alter a system with many particles significantly on a macroscopic level.
	{{Lead missing\|date=January 2011}}

	== Motivation ==		== Motivation ==
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	== The demon algorithm ==		== The demon algorithm ==

⚫	The ~~'''~~demon algorithm~~'''~~ is a Monte Carlo method for efficiently sampling members of a microcanonical ensemble with a given energy. An additional degree of freedom, called 'the demon', is added to the system and is able to store and provide energy. If a drawn microscopic state has lower energy than the original state, the excess energy is transferred to the demon. For a sampled state that has higher energy than desired, the demon provides the missing energy if it is available. The demon can not have negative energy and it does not interact with the particles beyond exchanging energy. Note that the additional degree of freedom of the demon does not alter a system with many particles significantly on a macroscopic level.

	The full procedure can be summarized by the following steps:		The full procedure can be summarized by the following steps: