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Carnot Cycle at Finite Power and Attainability of Maximal Efficiency Armen Allahverdyan (Yerevan Physics Institute ) -- Introduction: heat engines, Carnot cycle -- Non-equilibrium Carnot cycle -- Analysis: PRL 2013. -- Coauthors: Karen Hovhannisyan,

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slide1

Carnot Cycle at Finite Power and Attainability of Maximal Efficiency

Armen Allahverdyan

(Yerevan Physics Institute)

-- Introduction: heat engines, Carnot cycle

-- Non-equilibrium Carnot cycle

-- Analysis: PRL 2013.

-- Coauthors: Karen Hovhannisyan,

S. Gevorkian, A. Melkikh

slide2

Work-source

Hot bath

Cold bath

Cyclic engine

Power:

Work:

output / input

Efficiency:

Challenge: to make engines both powerful and efficient

B. Andresen, Angew Chem '11

U. Seifert, Rep. Prog. Phys. '12

Benenti, Casati, Prosen, Saito, arxiv:1311.4430

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Carnot cycle: useless in practice: 4 times slow

Thermally isolated and slow

Isothermal and slow

Carnot = maximal efficiency

slide4

Non-equilibrium Carnot cycle

Engine: density matrix and Hamiltonian

slide5

Work-source and baths act separately  easy to derive work and heat

Maximize W over dynamics

n+1 energy levels and the temperatures are fixed

slide6

Sudden changes are optimal

n degenerate states: energy concentration

optimized energy gaps

slide7

Work and efficiency

n>>1 number of levels

ln n >>1 number of particles

Relaxation time ?

Realistic

Ad hoc: system-bath (interaction) Hamiltonian is fine-tuned to system Hamiltonian

slide9

works for any

realistic

Unstructured data-base search (computationally complex)

Grover, PRL '97

Power  zero

Farhi, Gutman, PRA '98

Vogl, Schaller, Brandes, PRA'10

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ReduceW,resolve the degeneracy

Levinthal’s problem for protein folding

Zwanzig, PNAS '95

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Conclusions

The reason of not reaching Carnot efficiencyfor realistic system-bath interaction is computational complexity

Protein models as sub-optimal Carnot engine

Non-reachability of Carnot efficiency at a large power is not a law of nature: there is a fine-tuned interaction that achieves this.