Sample Qs

Question 1

Answer 1

Question 2

The Becker-Döring solution to the birth-death master equations of nucleation

Answer 2

Question 3

The master equations describing the birth-death process are

Answer 3

where βN and γN are transition probabilities, per unit time, that an N-cluster macrostate should gain or lose a particle, respectively

Question 4

What is probability current

Answer 4

Question 5

Discuss the concept of entropy production within a framework of stochastic thermodynamics, giving attention to the following points, and using diagrams to support your statements.

i. Describe the nature of the dynamics that control the system evolution.

Answer 5

i) The essiential information is that the system evolution is to be described using stochastic equations of motion, i.e. representing random interactions between system and environment.

Question 6

Discuss the concept of entropy production within a framework of stochastic thermodynamics, giving attention to the following points, and using diagrams to support your statements.

ii)Define the stochastic entropy production associated with a system trajectory

Answer 6

Question 7

iii. Derive an integral fluctuation relation involving the stochastic entropy production and use it to obtain an appropriate form for the second law of thermodynamics.

Answer 7

Question 8

Discuss the concept of entropy production within a framework of stochastic thermodynamics, giving attention to the following points, and using diagrams to support your statements.

iv. Explain the meaning of thermal equilibrium in a dynamical system using this framework.

Answer 8

Question 9

Explain what is meant by a potential of mean force

Answer 9

Question 10

coarse graining

Answer 10