Quantum thermodynamics

In the physical sciences, quantum thermodynamics is the study of heat and work dynamics in quantum systems. Approximately, quantum thermodynamics attempts to combine thermodynamics and quantum mechanics into a coherent whole. The essential point at which "quantum mechanics" began was when, in 1900, Max Planck outlined the "quantum hypothesis", i.e. that the energy of atomic systems can be quantized, as based on the first two laws of thermodynamics as described by Rudolf Clausius (1865) and Ludwig Boltzmann (1877). See the history of quantum mechanics for a more detailed outline.

Overview

A central objective in quantum thermodynamics is the quantitative and qualitative determination of the laws of thermodynamics at the quantum level in which uncertainty and probability begin to take effect. A fundamental question is: what remains of thermodynamics if one goes to the extreme limit of small quantum systems having a few degrees of freedom? If thermodynamics applies at this level, does the second law of thermodynamics remain unchanged, or is there a more universal formulation than the many existing formulations, such as: the entropy of a closed system cannot decrease; heat flows from high to low temperature; systems evolve towards minimum potential energy wells; energy tends to dissipate; and so on. The search for a more universal formulation of the second law of thermodynamics on the quantum level has perplexed physicists for many years. Mechanical (quantum) and equilibrium thermodynamics have long been developed separately for different fundamental reasons. In the past, each has been seemingly given its own domain to expand and has done so with great success. The problem arises when the kinematics and dynamics of the two systems (mechanical and equilibrium thermodynamics) are compared in relation to entropy and the second law of thermodynamics.A more universal description of the laws of thermodynamics is needed to rationalize the two seemingly conflicting notions of mechanical and equilibrium thermodynamics into relative subsets of a completely generalized law. Maxwell explained it thusly; “In dealing with masses of matter, while we do not perceive the individual molecules, we are compelled to adopt what I have described as the statistical method of calculation, and to abandon the strict dynamical method, in which we follow every molecule by the calculus”. This is known as Maxwell’s intelligent demon. The statistical method Maxwell was talking about is now known as statistical mechanics. Though statistical mechanics does well in furthering the search for a more generalized view of thermodynamics and has produced many beneficial results including the Boltzmann equation, the Onsager reciprocity relations, the fluctuation- dissipation, relations, and the Master equations, the narrow, selective approach of statistical mechanics has yet to produce a general theory of compromise between mechanics and equilibrium thermodynamics.

Keenan Thermodynamics

The keenan School of thermodynamics at MIT (named for physicist Joseph H. Keenan) seeks to provide a solution to the mechanical verses equilibrium thermodynamics problem while still maintaining the formalism implied by the traditional structure of physical theory without abandoning the concepts of the state of a system that is found when statistical mechanics is closely scrutinized. Mechanical Engineers George N. Hatsopoulos and Eilas P. Gyftopoulos have done an extensive amount of work trying to solve this puzzle and, as a result, formulated a resolution of a unified quantum theory of mechanics and thermodynamics. Unlike statistical mechanics, this theory does not abandon any traditional concepts of physical theory, but encompasses all systems and all states. The unified quantum theory contains seven different features that distinguish it from statistical mechanics.

i) The quantum mechanical density operators ρ ≥ ρ2 can be represented by a homogeneous ensemble. This ensemble holds that every member is assigned the same ρ as any other member. This ρ cannot be experimentally decomposed. This means that ρ is both unambiguous and irreducible.

ii) The unified quantum theory also notes that the Schrödinger equation is correct, yet incomplete. The Schrödinger equation is currently only defined for zero entropy situations in time that are fundamentally reversible. This is also true for the von Neumann equation of motion.

iii) The unified quantum theory presents the only analytical expression for entropy that satisfies the following criteria. It is time invariant; defined for every system (including stable and not stable equilibrium states); invariant in all reversible adiabatic processes and increases in all irreversible adiabatic processes; additive for all systems and states; non negative for states with probabilities described by a projector ρ = ρ2, have a unique value for given energy; constituents, or parameters if the state is in equilibrium; the graph of entropy vs energy must be smooth for stable equilibrium states; if a system is composed of two systems in mutual stable equilibrium, then it must yield the same temperatures, total potentials, and pressures of the composite system; it must reduce to previously experimentally established relations that express the entropy in terms of values of energy, amounts of constituents, and parameters.

iv) The unified quantum theorem is not restricted to thermodynamic equilibrium states.

v) Unlike the projectors of the heterogeneous ensemble established in statistical mechanics, the projectors of the homogeneous ensemble are not restricted to being treated as both time independent and dependant.

vi) The entropy of quantum thermodynamics is a measure of the spatial shape of the constituents of the system in any state.

vii) Where statistical mechanics claims that the entropy of a stable equilibrium system represents the ultimate disorder of the system, the unified quantum theory claims that it represents perfect order of the system.

See also

• Quantum decoherence

Further reading

1. Gemmer, J., Michel, M., Mahler, G. (2005). Quantum Thermodynamics – Emergence of Thermodynamic Behavior Within Composite Quantum Systems. Springer. ISBN 3-540-22911-6. 
2. Rudakov, E.S. (1998). Molecular, Quantum and Evolution Thermodynamics: Development and Specialization of the Gibbs Method.. Donetsk State University Press. ISBN 966-02-0708-5. 

External links

• Quantum Thermodynamics and the Gibbs Paradox
• Quantum Thermodynamics
• On the Classical Limit of Quantum Thermodynamics in Finite Time [PDF-format]
• Quantum Thermodynamics - list of good related articles