Uncertainty relations of Statistical Mechanics

TL;DR

This paper explores the fundamental uncertainty and complementarity between thermodynamic quantities like energy and temperature, extending the concept to systems with multiple control parameters.

Contribution

It generalizes previous ideas of thermodynamic uncertainty relations to systems with several control parameters, building on the concept of complementarity in statistical mechanics.

Findings

Establishes a thermodynamic uncertainty relation for multiple control parameters.

Demonstrates the impossibility of simultaneously measuring energy and temperature precisely.

Extends the complementarity concept to more complex thermodynamic systems.

Abstract

Recently, we have presented some simple arguments supporting the existence of certain complementarity between thermodynamic quantities of temperature and energy, an idea suggested by Bohr and Heinsenberg in the early days of Quantum Mechanics. Such a complementarity is expressed as the impossibility of perform an exact simultaneous determination of the system energy and temperature by using an experimental procedure based on the thermal equilibrium with other system regarded as a measure apparatus (thermometer). In this work, we provide a simple generalization of this latter approach with the consideration of a thermodynamic situation with several control parameters.