Carnot Cycle at Finite Power and Attainability of Maximal Efficiency
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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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Carnot Cycle at Finite Power and Attainability of Maximal Efficiency Armen Allahverdyan

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Carnot cycle at finite power and attainability of maximal efficiency armen allahverdyan

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


Carnot cycle at finite power and attainability of maximal efficiency armen allahverdyan

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


Carnot cycle at finite power and attainability of maximal efficiency armen allahverdyan

Carnot cycle: useless in practice: 4 times slow

Thermally isolated and slow

Isothermal and slow

Carnot = maximal efficiency


Carnot cycle at finite power and attainability of maximal efficiency armen allahverdyan

Non-equilibrium Carnot cycle

Engine: density matrix and Hamiltonian


Carnot cycle at finite power and attainability of maximal efficiency armen allahverdyan

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


Carnot cycle at finite power and attainability of maximal efficiency armen allahverdyan

Sudden changes are optimal

n degenerate states: energy concentration

optimized energy gaps


Carnot cycle at finite power and attainability of maximal efficiency armen allahverdyan

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


Carnot cycle at finite power and attainability of maximal efficiency armen allahverdyan

An example of fine-tuned system-bath Hamiltonian

bath: 2-level systems

there is


Carnot cycle at finite power and attainability of maximal efficiency armen allahverdyan

works for any

realistic

Unstructured data-base search (computationally complex)

Grover, PRL '97

Power  zero

Farhi, Gutman, PRA '98

Vogl, Schaller, Brandes, PRA'10


Carnot cycle at finite power and attainability of maximal efficiency armen allahverdyan

ReduceW,resolve the degeneracy

Levinthal’s problem for protein folding

Zwanzig, PNAS '95


Carnot cycle at finite power and attainability of maximal efficiency armen allahverdyan

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.


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