quantum thermodynamics

History

The foundations of ordinary thermodynamics were laid by Ludwig Boltzmann in the 19th century. Quantum thermodynamics began to develop from the mid-20th century when scientists started combining quantum mechanics (discovered by Erwin Schrödinger and others) with ideas about heat.

How it works

Two connected vessels with one gas atom each — this is how quantum heat exchange can be seen. The atom tunnels (passes through an invisible barrier, as if seeping) from one vessel to another, transferring energy in jumps rather than smoothly. Quantum thermodynamics describes such jumps using mathematics where probabilities and special states play a key role.

History

The foundations of ordinary thermodynamics were laid by Ludwig Boltzmann in the 19th century. Quantum thermodynamics began to develop from the mid-20th century when scientists started combining quantum mechanics (discovered by Erwin Schrödinger and others) with ideas about heat.

How it works

Two connected vessels with one gas atom each — this is how quantum heat exchange can be seen. The atom tunnels (passes through an invisible barrier, as if seeping) from one vessel to another, transferring energy in jumps rather than smoothly. Quantum thermodynamics describes such jumps using mathematics where probabilities and special states play a key role.

History

Thermodynamics as a phenomenological science emerged in the 19th century thanks to the works of Sadi Carnot, Rudolf Clausius, and Lord Kelvin. Statistical justification was provided by Ludwig Boltzmann, linking entropy to the number of microstates (formula S = k log W). The quantum era required a revision of these ideas, starting with the work of von Neumann, who introduced the entropy S(ρ) = −Tr(ρ ln ρ) and showed its role in measurement. In the 1950s, the development of the theory of open quantum systems and lasers stimulated interest in the thermodynamics of small systems. The field acquired its modern form in the 1990s–2000s after the proof of fluctuation theorems (Jarzynski, Crooks) and their quantum generalizations. Today, quantum thermodynamics is actively developing in the context of quantum computing and nanotechnology.

How it works

Quantum thermodynamics is based on the description of a system through the density matrix ρ, which generalizes the classical probability distribution. The equilibrium state is given by the Gibbs distribution: ρ_eq = e^{-βH} / Z, where Z = Tr(e^{-βH}) is the partition function, β = 1/(k_B T). Entropy is given by the von Neumann entropy S_vN = −k_B Tr(ρ ln ρ). Work and heat are defined as changes in the internal energy U = Tr(ρH) with the separation of contributions from changes in the Hamiltonian H (work) and from changes in the density matrix (heat). In non-equilibrium processes, the quantum fluctuation theorem applies: the probability of obtaining work W in the forward process and −W in the reverse are related by P_f(W)/P_r(−W) = e^{β(W−ΔF)}. This expresses the universality of fluctuations and allows testing the laws of thermodynamics at the level of single quantum transitions. Additionally, quantum correlations (entanglement) can enhance the efficiency of heat engines by using non-classical states of the working body.

Open problems & fun facts

Development of a complete thermodynamics for systems with strongly entangled states and coherence; Understanding the limits of extracting work from quantum information (Landauer's principle in the quantum regime); Creation of experimental quantum heat engines with superiority over classical counterparts; Elucidation of the role of gravity in quantum thermodynamics and the black hole information paradox; Quantum batteries and the problem of fast charging without degradation

💡 According to the equality theorem for quantum systems, one can measure the free energy difference between two states by repeatedly performing a rapid non-equilibrium transition and averaging the exponential of the work, even if the process is far from equilibrium. This is like determining the average maturity of wine by opening a sample at a random moment of fermentation.