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Introduction to Nonequilibrium Thermodynamics

Introduction to Nonequilibrium Thermodynamics
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Dr.SamuelHunt,United Arab Emirates,Teacher
Published Date:21-07-2017
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Introduction to Nonequilibrium Thermodynamics: From Onsager to Micromotors Based on the lecture “Nonequilibrium phenomena in micro and nanosystems” taught at Freie Universität Berlin Jan Korbel Faculty of Nuclear Sciences and Physical Engineering, CTU, Prague 6th Student Colloquium and School on Mathematical Physics,Stará Lesná 25. 8. 2012 1 / 23Outline  History & Motivation  Introduction to nonequilibrium thermodynamics  Application: Brownian motors  Recent developments in nonequilibrium TD 2 / 23History & Motivation  Theory of nonequilibrium thermodynamics originates from the first half of 20. century  It was mainly developed by Onsager, Rayleigh...  Aim: to extend a formalism of equilibrium processes to dissipative or fast processes  Many processes observed in real system exhibit behavior of irreversible processes  Applications: biophysics, nanosystems,... 3 / 23 General laws  System-specific response coefficients: c ;c ; ;::: p v T  Description of macroscopic systems  Small fluctuations can be neglected p E N 1 ' 'p (1) E N N  Equilibrium: state of a system, where we cannot observe any change of measurable quantities  Structure of Thermodynamics: Equilibrium thermodynamics Basic notes 4 / 23 General laws  System-specific response coefficients: c ;c ; ;::: p v T  Equilibrium: state of a system, where we cannot observe any change of measurable quantities  Structure of Thermodynamics: Equilibrium thermodynamics Basic notes  Description of macroscopic systems  Small fluctuations can be neglected p E N 1 ' 'p (1) E N N 4 / 23 General laws  System-specific response coefficients: c ;c ; ;::: p v T  Structure of Thermodynamics: Equilibrium thermodynamics Basic notes  Description of macroscopic systems  Small fluctuations can be neglected p E N 1 ' 'p (1) E N N  Equilibrium: state of a system, where we cannot observe any change of measurable quantities 4 / 23Equilibrium thermodynamics Basic notes  Description of macroscopic systems  Small fluctuations can be neglected p E N 1 ' 'p (1) E N N  Equilibrium: state of a system, where we cannot observe any change of measurable quantities  Structure of Thermodynamics:  General laws  System-specific response coefficients: c ;c ; ;::: p v T 4 / 23Equilibrium thermodynamics Laws of thermodynamics  First law (Claussius 1850, Helmholtz 1847): Energy is conserved. dU =QW (2)  Second law (Carnot 1824, Claussius 1854, Kelvin): Heat cannot be fully transformed into work. Q dS (3) T  Third law: We cannot bring the system into the absolute zero temperature in a finite number of steps. 5 / 23Equilibrium thermodynamics Laws of thermodynamics  First law (Claussius 1850, Helmholtz 1847): Energy is conserved. dU =QW (2)  Second law (Carnot 1824, Claussius 1854, Kelvin): Heat cannot be fully transformed into work. Q dS (3) T  Third law: We cannot bring the system into the absolute zero temperature in a finite number of steps. 5 / 23 For quasistatic reversible process we have   X dU S R dS = + Y dX Y = (4) R i i i T X i i Q  From the second law we know that S = R T Q  For irreversible process we get an extra entropy S = + S i T where S 0 i  Entropy production rate: X dS S X i = (5) dt X t i i  aim of Nonequilibrium TD: to compute entropy production rate Nonequilibrium thermodynamics 6 / 23Q  For irreversible process we get an extra entropy S = + S i T where S 0 i  Entropy production rate: X dS S X i = (5) dt X t i i  aim of Nonequilibrium TD: to compute entropy production rate Nonequilibrium thermodynamics  For quasistatic reversible process we have   X dU S R dS = + Y dX Y = (4) R i i i T X i i Q  From the second law we know that S = R T 6 / 23 Entropy production rate: X dS S X i = (5) dt X t i i  aim of Nonequilibrium TD: to compute entropy production rate Nonequilibrium thermodynamics  For quasistatic reversible process we have   X dU S R dS = + Y dX Y = (4) R i i i T X i i Q  From the second law we know that S = R T Q  For irreversible process we get an extra entropy S = + S i T where S 0 i 6 / 23 aim of Nonequilibrium TD: to compute entropy production rate Nonequilibrium thermodynamics  For quasistatic reversible process we have   X dU S R dS = + Y dX Y = (4) R i i i T X i i Q  From the second law we know that S = R T Q  For irreversible process we get an extra entropy S = + S i T where S 0 i  Entropy production rate: X dS S X i = (5) dt X t i i 6 / 23Nonequilibrium thermodynamics  For quasistatic reversible process we have   X dU S R dS = + Y dX Y = (4) R i i i T X i i Q  From the second law we know that S = R T Q  For irreversible process we get an extra entropy S = + S i T where S 0 i  Entropy production rate: X dS S X i = (5) dt X t i i  aim of Nonequilibrium TD: to compute entropy production rate 6 / 23 There exists no unified theory of nonequilibrium thermodynamics.  Near equilibrium exists a linear theory that is universal.  Let us consider a system which we divide into small subsystems. We assume that every system is in local equilibirium a a b b  Total entropy is: S = S (X ) +S (X ) +::: i i  Entropy production rate for a subsystema: a X X dS a a a a a _  = = Y X = Y J (6) i i i i dt i i Nonequilibrium thermodynamics Linear thermodynamics 7 / 23 Near equilibrium exists a linear theory that is universal.  Let us consider a system which we divide into small subsystems. We assume that every system is in local equilibirium a a b b  Total entropy is: S = S (X ) +S (X ) +::: i i  Entropy production rate for a subsystema: a X X dS a a a a a _  = = Y X = Y J (6) i i i i dt i i Nonequilibrium thermodynamics Linear thermodynamics  There exists no unified theory of nonequilibrium thermodynamics. 7 / 23 Let us consider a system which we divide into small subsystems. We assume that every system is in local equilibirium a a b b  Total entropy is: S = S (X ) +S (X ) +::: i i  Entropy production rate for a subsystema: a X X dS a a a a a _  = = Y X = Y J (6) i i i i dt i i Nonequilibrium thermodynamics Linear thermodynamics  There exists no unified theory of nonequilibrium thermodynamics.  Near equilibrium exists a linear theory that is universal. 7 / 23a a b b  Total entropy is: S = S (X ) +S (X ) +::: i i  Entropy production rate for a subsystema: a X X dS a a a a a _  = = Y X = Y J (6) i i i i dt i i Nonequilibrium thermodynamics Linear thermodynamics  There exists no unified theory of nonequilibrium thermodynamics.  Near equilibrium exists a linear theory that is universal.  Let us consider a system which we divide into small subsystems. We assume that every system is in local equilibirium 7 / 23Nonequilibrium thermodynamics Linear thermodynamics  There exists no unified theory of nonequilibrium thermodynamics.  Near equilibrium exists a linear theory that is universal.  Let us consider a system which we divide into small subsystems. We assume that every system is in local equilibirium a a b b  Total entropy is: S = S (X ) +S (X ) +::: i i  Entropy production rate for a subsystema: a X X dS a a a a a _  = = Y X = Y J (6) i i i i dt i i 7 / 23ab a b  := Y Y is affinity i i i  Affinity - deviation from equilibrium TD force  A system brought from equilibrium reacts by creating a current X J = L (7) i ij j j  L nonequilibrium response coefficients ij  Generally are L functions of ’s, but near equilibrium are assumed to ij be constants - J ’s are linear functions of ’s i Nonequilibrium thermodynamics Current and Affinity a a  J is generalized current, at equilibrium J = 0 i i 8 / 23