Quantum Thermodynamics
2.997 Advanced Topics in
Mechanical Engineering
Explores the
foundations of thermodynamics from a quantum theory point of view, by
developing a unified theory of mechanics and thermodynamics and a general
quantum equation of motion for reversible and irreversible processes from which
the second law emerges as a general dynamical theorem. Topics include nonequilibrium and stable
equilibrium states of qubits, qudits, and fermion and boson fields;
entanglement, entropy, singleparticle quantum heat engines, and open
conceptual issues in quantum statistical mechanics and quantum theory of open
systems. Emphasis on conceptual definitions. logical consistency, and rigorous
mathematicalphysics approach.
Selfcontained
reviews of the necessary background in classical and quantum mechanics, general
thermodynamics principles and linear algebra.
Graduate
students from all science and engineering courses welcome.
Contact instructor for permission. Email:
Course
material: handouts plus few papers among those available at http://www.quantumthermodynamics.org/
Definition of the fundamental concepts of

system

physical observable or property

preparation

homogeneous vs heterogeneous preparation

state

mean value of an observable

expectation values for a heterogeneous preparation
and their mathematical representations in

Classical Mechanics

Classical Statistical Mechanics

Quantum Mechanics

Quantum Statistical Mechanics

Quantum Thermodynamics

Quantum Statistical Thermodynamics
Observables and measurements

quantum "questions" and "answers"

quantum (Heinsenberg and SchroedingerRobertson) uncertainties

coherent states

complete set or "quorum" of observables

measurement of the state, quantum tomography

"pure" and "mixed" states

correlation

entanglement

Bloch sphere representation for a twolevel system (qubit)
Hamiltonian dynamics in

Classical Mechanics: Hamilton equations of motion

Quantum Mechanics: Schroedinger equation of motion

Quantum Thermodynamics: von Neumann equation of motion

Energy and the generator of Hamiltonian dynamics

stability of the equilibrium states

timeenergy uncertainty relations
(Quantum Thermo)Dynamics of a single constituent of matter: general
equation of motion for reversible and irreversible processes

generators of the motion

constants of the motion

nondissipative states and limit cycles

equilibrium states

conservation of cardinality of the density operator

von Neumann entropy functional

rate of entropy increase for a strictly isolated and uncorrelated
system, irreversibility

unstable equilibrium states

stable equilibrium states and their uniqueness (second law)

Onsager reciprocity relations as general features of the dissipative
part of the dynamics

application to a twolevel system (quibit)

application to a dlevel system (qudit)

timeenergy and timeentropy uncertainty relations

Carnot and Ottolike quantum heatengine cycles for a single spin1/2
system

application to a quantum "field" of indistinguishable
particles

bosons and fermions

BoseEinstein and FermiDirac distributions at stable equilibrium

occupation numbers and spontaneous irreversible internal redistribution
(Quantum Thermo)Dynamics of a composite system

reduced density operators

separability and locality

relaxation and decoherence

correlations and entanglement

entropybased and other measures of correlation

general equation of motion for a composite system and main features

relation with master equations of KossakowskiLindblad form
Discussions of the following or other issues at students' request:

thermodynamic adiabatic availability versus Hamiltonian unitary
availability ("ergotropy")

general indicators of entanglement

fluctuations improperly interpreted as second law violations

Maxwell demons and quantum ratchets

single particle tests of quantum theory

SchroedingerPark "paradox" about the concept of state in
Quantum Statistical Mechanics