Determination of Nonequilibrium Temperature and Pressure using Clausius Equality in a State with Memory: A Simple Model Calculation

TL;DR

This paper introduces a method to determine nonequilibrium temperature and pressure using Clausius equality in a quantum system with memory, demonstrating the persistence of memory effects in quantum free expansion.

Contribution

It presents the first calculation of nonequilibrium temperature and pressure in a quantum free expansion with memory, validating the formulation through independent comparison.

Findings

Nonequilibrium temperature and pressure can be determined from quantum evolution.

Memory effects persist and prevent thermalization in the system.

The formulation is consistent with independent ratio comparisons.

Abstract

Use of the extended definition of heat dQ=deQ+diQ converts the Clausius inequality dS greater than or equal to deQ/T0 into an equality dS=dQ/T involving the nonequilibrium temperature T of the system having the conventional interpretation that heat flows from hot to cold. The equality is applied to the exact quantum evolution of a 1-dimensional ideal gas free expansion. In a first ever calculation of its kind in an expansion which retains the memory of initial state, we determine the nonequilibrium temperature T and pressure P, which are then compared with the ratio P/T obtained by an independent method to show the consistency of the nonequilibrium formulation. We find that the quantum evolution by itself cannot eliminate the memory effect.cannot eliminate the memory effect; hence, it cannot thermalize the system.