Course Identification

Quantum Thermodynamics and Open Systems

Lecturers and Teaching Assistants

Prof. Gershon Kurizki, Prof. Ronnie Kozlov
Avijit Misra

Course Schedule and Location

Second Semester
Wednesday, 14:15 - 17:00, FGS, Rm A

Field of Study, Course Type and Credit Points

Chemical Sciences: Lecture; Elective; 2.00 points
Physical Sciences: Lecture; Elective; 2.00 points
Chemical Sciences (Materials Science Track): Lecture; Elective; 2.00 points


The grades for the course will be composed of 2 exercises and a written discussion.





Language of Instruction


Attendance and participation

Expected and Recommended

Grade Type

Numerical (out of 100)

Grade Breakdown (in %)


Evaluation Type

Final assignment

Scheduled date 1


Estimated Weekly Independent Workload (in hours)



1. Open Systems: Decoherence and Measurement

a. Quantum measurements and decoherence

b. Markovian decoherence dynamics b master equations


2. Non-Markovian Decoherence

a. Non-Markovian dynamics

b. Quantum Zeno anti-Zeno effects


3. Decoherence as Loss of Reversibility

a. Decoherence and reversibility: Quantum Zeno and anti-Zeno effects

b. Projection operator master equations


4. Protection from Decoherence

a. Decoherence free subspaces

b. Dynamical control of Decoherence


5. The Principles of Thermodynamics for Quantum Systems

a. The Carnot and Maximum-Power Bonds for Quantum Heat Machines

b. The Third Law as Absolut-Zero Unattainability

c. Work-information Trade-off and the Szilard-Landauer (SL) Bound


6. Machine Cycles under Periodic Modulation

a. Floquet Expansion of the Markovian (Lindblad) Master Equation

b. Course-Grained Evolution: From Non-Markovian to Markovian Dynamics

c. Heat Currents and Power: Strokes and Continuous Cycles


7. Quantum Heat Machines driven by a Quantum Piston

a. Work and Heat in Fully Quantized Setups

b. Refrigeration Efficiency Bound with a Quantized Piston


8. Cooling Speed of Quantum Baths

a. Cooling-Rate Scaling with Temperature

b. Cooling-Rate Dependence on Bath Dispersion

9. Control of Non-Markovian Thermodynamic Processes

a. Impulsive Perturbations of Equilibrium State

b. Post measurement Evolution: Alternation Heating and Cooling

c. Non-monotonic Entropy Evolutions: Spohn’s Theorem Violation


10. Work-Information Relation under Non-Markovian Evolution

a. The SL Bond Revisited

b. Work-Information Relation for a Non-Markovian Cycle


Learning Outcomes

Upon successful completion of this course students should be able to:

  1. Explain the fundamental concepts of open quantum systems, such as entanglement, measurement theory and system-bath interaction.
  2. Analyze different de-coherence mechanisms in several experimental systems.
  3. Evaluate the Quantumness of several phenomena, such as teleportation, interaction-free measurement and coherent control of quantum thermodynamics.
  4. Formulate their own research topics using concepts and methods learnt.

Reading List