What Is the Temperature? Modern Outlook on the Concept of Temperature

TL;DR

This paper explores the fundamental nature and broad applicability of temperature across classical, quantum, and relativistic physics, emphasizing its conceptual depth and implications in cosmology and information theory.

Contribution

It provides a modern perspective on temperature, extending its definition to small, non-interacting systems and linking it to quantum, relativistic, and cosmological contexts.

Findings

Temperature can be defined for systems with few particles.

The Kelvin scale applies in quantum and relativistic regimes.

Temperature relates to the geometry of configurational space.

Abstract

The meaning and evolution of the notion of "temperature" (which is a key concept for the condensed and gaseous matter theories) are addressed from the different points of view. The concept of temperature turns out to be much more fundamental than it is conventionally thought. In particular, the temperature may be introduced for the systems built of "small" number of particles and particles in rest. The Kelvin temperature scale may be introduced into the quantum and relativistic physics due to the fact, that the efficiency of the quantum and relativistic Carnot cycles coincides with that of the classical one. The relation of the temperature to the metrics of the configurational space describing the behavior of the system built from non-interacting particles is demonstrated. The Landauer principle asserts that the temperature of the system is the only physical value defining the energy cost of isothermal erasing of the single bit of information. The role of the temperature the cosmic microwave background in modern cosmology is discussed.