In 1905, Albert Einstein argued that the requirement of consistency between thermodynamics and electromagnetism[3] leads to the conclusion that light is quantized, obtaining the relation
[5] Quantum mechanics inserts dynamics into thermodynamics, giving a sound foundation to finite-time-thermodynamics.
The main assumption is that the entire world is a large closed system, and therefore, time evolution is governed by a unitary transformation generated by a global Hamiltonian.
This assumption is used to derive the Kubo-Martin-Schwinger stability criterion for thermal equilibrium i.e. KMS state.
This approach represents a thermodynamic idealization: it allows energy transfer, while keeping a tensor product separation between the system and bath, i.e., a quantum version of an isothermal partition.
This observation is particularly important in the context of quantum thermodynamics, where it is tempting to study Markovian dynamics with an arbitrary control Hamiltonian.
Erroneous derivations of the quantum master equation can easily lead to a violation of the laws of thermodynamics.
For a slow change, one can adopt the adiabatic approach and use the instantaneous system’s Hamiltonian to derive
A reexamination of the time-dependent heat current expression using quantum transport techniques has been proposed.
[13] Phenomenological formulations of irreversible quantum dynamics consistent with the second law and implementing the geometric idea of "steepest entropy ascent" or "gradient flow" have been suggested to model relaxation and strong coupling.
[14][15] The second law of thermodynamics is a statement on the irreversibility of dynamics or, the breakup of time reversal symmetry (T-symmetry).
This should be consistent with the empirical direct definition: heat will flow spontaneously from a hot source to a cold sink.
From a static viewpoint, for a closed quantum system, the 2nd law of thermodynamics is a consequence of the unitary evolution.
In thermodynamics, entropy is related to the amount of energy of a system that can be converted into mechanical work in a concrete process.
is the Shannon entropy with respect to the possible outcomes: The most significant observable in thermodynamics is the energy represented by the Hamiltonian operator
[21] John von Neumann suggested to single out the most informative observable to characterize the entropy of the system.
[22] In 2018 has been shown that, by correctly taking into account all work and energy contributions in the full system, local master equations are fully coherent with the second law of thermodynamics.
A quantum version of an adiabatic process can be modeled by an externally controlled time dependent Hamiltonian
The quantum adiabatic condition is therefore equivalent to no net change in the population of the instantaneous energy levels.
When the adiabatic conditions are not fulfilled, additional work is required to reach the final control value.
In this case, quantum friction can be suppressed using shortcuts to adiabaticity as demonstrated in the laboratory using a unitary Fermi gas in a time-dependent trap.
[24] The coherence stored in the off-diagonal elements of the density operator carry the required information to recover the extra energy cost and reverse the dynamics.
The second formulation, known as the unattainability principle can be rephrased as;[28] The dynamics of the cooling process is governed by the equation: where
The basic idea of quantum typicality is that the vast majority of all pure states featuring a common expectation value of some generic observable at a given time will yield very similar expectation values of the same observable at any later time.
This is meant to apply to Schrödinger type dynamics in high dimensional Hilbert spaces.
As a consequence individual dynamics of expectation values are then typically well described by the ensemble average.
[30] The second law of thermodynamics can be interpreted as quantifying state transformations which are statistically unlikely so that they become effectively forbidden.
The second law typically applies to systems composed of many particles interacting; Quantum thermodynamics resource theory is a formulation of thermodynamics in the regime where it can be applied to a small number of particles interacting with a heat bath.
For processes which are cyclic or very close to cyclic, the second law for microscopic systems takes on a very different form than it does at the macroscopic scale, imposing not just one constraint on what state transformations are possible, but an entire family of constraints.
Some of them involve subtle quantum coherence or correlation effects,[33][34][35] while others rely solely on nonthermal classical probability distribution functions.