Quantum thermodynamics
Encyclopedia
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.
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.
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 comprised 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.
Heat
In physics and thermodynamics, heat is energy transferred from one body, region, or thermodynamic system to another due to thermal contact or thermal radiation when the systems are at different temperatures. It is often described as one of the fundamental processes of energy transfer between...
and work
Work (thermodynamics)
In thermodynamics, work performed by a system is the energy transferred to another system that is measured by the external generalized mechanical constraints on the system. As such, thermodynamic work is a generalization of the concept of mechanical work in mechanics. Thermodynamic work encompasses...
dynamics in quantum systems. Approximately, quantum thermodynamics attempts to combine thermodynamics
Thermodynamics
Thermodynamics is a physical science that studies the effects on material bodies, and on radiation in regions of space, of transfer of heat and of work done on or by the bodies or radiation...
and quantum mechanics
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
into a coherent whole. The essential point at which "quantum mechanics" began was when, in 1900, Max Planck
Max Planck
Max Karl Ernst Ludwig Planck, ForMemRS, was a German physicist who actualized the quantum physics, initiating a revolution in natural science and philosophy. He is regarded as the founder of the quantum theory, for which he received the Nobel Prize in Physics in 1918.-Life and career:Planck came...
outlined the "quantum hypothesis", i.e. that the energy of atomic systems can be quantized, as based on the first two laws of thermodynamics
Laws of thermodynamics
The four laws of thermodynamics summarize its most important facts. They define fundamental physical quantities, such as temperature, energy, and entropy, in order to describe thermodynamic systems. They also describe the transfer of energy as heat and work in thermodynamic processes...
as described by Rudolf Clausius
Rudolf Clausius
Rudolf Julius Emanuel Clausius , was a German physicist and mathematician and is considered one of the central founders of the science of thermodynamics. By his restatement of Sadi Carnot's principle known as the Carnot cycle, he put the theory of heat on a truer and sounder basis...
(1865) and Ludwig Boltzmann
Ludwig Boltzmann
Ludwig Eduard Boltzmann was an Austrian physicist famous for his founding contributions in the fields of statistical mechanics and statistical thermodynamics...
(1877). See the history of quantum mechanics
History of quantum mechanics
The history of quantum mechanics, as it interlaces with the history of quantum chemistry, began essentially with a number of different scientific discoveries: the 1838 discovery of cathode rays by Michael Faraday; the 1859-1860 winter statement of the black body radiation problem by Gustav...
for a more detailed outline.
Overview
A central objective in quantum thermodynamics is the quantitative and qualitative determination of the laws of thermodynamicsLaws of thermodynamics
The four laws of thermodynamics summarize its most important facts. They define fundamental physical quantities, such as temperature, energy, and entropy, in order to describe thermodynamic systems. They also describe the transfer of energy as heat and work in thermodynamic processes...
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
Second law of thermodynamics
The second law of thermodynamics is an expression of the tendency that over time, differences in temperature, pressure, and chemical potential equilibrate in an isolated physical system. From the state of thermodynamic equilibrium, the law deduced the principle of the increase of entropy and...
remain unchanged, or is there a more universal formulation than
the many existing formulations, such as: the entropy
Entropy
Entropy is a thermodynamic property that can be used to determine the energy available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when...
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
Second law of thermodynamics
The second law of thermodynamics is an expression of the tendency that over time, differences in temperature, pressure, and chemical potential equilibrate in an isolated physical system. From the state of thermodynamic equilibrium, the law deduced the principle of the increase of entropy and...
.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 comprised 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.
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