Thermodynamics and Statistical Physics

Thermodynamics and statistical physics provide complementary frameworks for describing many-particle systems. Thermodynamics identifies a small set of macroscopic variables—energy, entropy, volume, particle number—and postulates relations such as the first and second laws, governing energy conservation and the increase of entropy. Statistical physics explains these laws in terms of the microscopic degrees of freedom. In the microcanonical ensemble, all accessible microstates at fixed energy, volume and particle number are equally probable, and the entropy emerges as the logarithm of the state count. Allowing energy exchange with a heat bath leads to the canonical ensemble, where the probability of each microstate is weighted by the Boltzmann factor. Key constructs include the partition function, from which free energies, average energies, entropies and response coefficients are derived. Equipartition links quadratic degrees of freedom to k_BT/2 per mode, while fluctuations are controlled by second derivatives of thermodynamic potentials. Phase transitions arise when interactions between particles produce singularities or non-analytic behaviour in these potentials as system size tends to infinity. Mean-field theories, Landau expansions and renormalisation-group techniques classify universality classes and critical exponents. Extensions to nonequilibrium and driven systems employ generalised Langevin equations, fluctuation theorems and formalisms such as GENERIC to account for memory, dissipation and entropy production. Together, these principles underpin the design and analysis of engines, refrigerators, materials and complex fluids across scales.

Research from Nature Portfolio

A disordered two-dimensional superconducting thin film was studied under magnetic-field–temperature mapping of the Nernst effect. A “ghost-temperature” line was identified, marking a thermal-to-quantum crossover of superconducting fluctuations within an anomalous metallic regime. The ghost-temperature intercept at zero temperature defines a broadened quantum critical ground state of the superconductor–insulator transition, revealing that the metallic phase corresponds to a critical region rather than a distinct thermodynamic phase.

In quantum resource theories, it has been shown that reversible interconversion of all resource states becomes possible through probabilistic protocols whose success probability remains bounded away from zero even asymptotically. This establishes a unique entropic measure as the rate-governing quantity under resource-non-generating operations and unifies deterministic and probabilistic paradigms. The findings refine the boundaries of quantum thermodynamics by demonstrating reversibility at the cost of non-zero failure probability.

Research from all publishers

A recent theoretical study derived an exact generalised Langevin equation for a driven Brownian particle in a solvent, demonstrating that nonequilibrium external forces induce an additional memory-dependent solvent-response force. This correction quantifies departures from standard fluctuation–dissipation relations and alters the effective drag, with implications for understanding driven colloids and molecular motors.

Developments in two-dimensional fluid models with broken parity symmetry have uncovered novel Hamiltonian structures that couple reversible dynamics with dissipative effects. By formulating vorticity dynamics in chiral active fluids within a unified Poisson-bracket and gradient-flow framework, researchers have elucidated how topological constraints and time-reversal asymmetry shape transport coefficients and stress responses in complex fluids.

Thermodynamics and Statistical Physics publication trend

The graph below shows the total number of articles in thermodynamics and statistical physics across all publications each year (not limited to Nature Index journals).

Technical terms

Partition function: Sum over microstates of the Boltzmann factor, encoding all equilibrium thermodynamic information.

Entropy: Measure of the logarithm of the number of accessible microstates or of information uncertainty in a probability distribution.

Free energy: Thermodynamic potential (Helmholtz or Gibbs) whose minimisation under given constraints yields equilibrium states.

Ensemble: Collection of virtual copies of a system subject to specified constraints (microcanonical, canonical, grand canonical).

Phase transition: Non-analytic change in thermodynamic properties as a control parameter (temperature, field) crosses a critical value.

Fluctuation–dissipation relation: Link between spontaneous equilibrium fluctuations and the linear response to external perturbations.

References

1. Broadened quantum critical ground state in a disordered superconducting thin film. Nature Communications (2024).
2. Reversibility of quantum resources through probabilistic protocols. Nature Communications (2024).
3. Nonequilibrium solvent response force: What happens if you push a Brownian particle. Physical Review Research (2024).
4. Hamiltonian structure of 2D fluid dynamics with broken parity. SciPost Physics (2023).
5. GENERIC framework for reactive fluid flows. ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik (2022).