The Carnot Cycle for Small Systems: Irreversibility and the Cost of Operations

TL;DR

This paper analyzes the Carnot cycle at small scales using stochastic energetics, revealing sources of irreversibility and discussing fundamental limits on energy conversion efficiency due to fluctuations and process distortions.

Contribution

It introduces a detailed stochastic framework to re-examine the Carnot cycle, highlighting irreversibility sources at microscopic scales without assuming thermodynamic limit.

Findings

Connection and disconnection to heat baths cause irreversibility.

Adiabatic processes distort energy distributions, leading to irreversibility.

Efficiency over many cycles exhibits null-recurrence, limiting perpetual energy machines.

Abstract

We employ the recently developed framework of the energetics of stochastic processes (called `stochastic energetics'), to re-analyze the Carnot cycle in detail, taking account of fluctuations, without taking the thermodynamic limit. We find that both processes of connection to and disconnection from heat baths and adiabatic processes that cause distortion of the energy distribution are sources of inevitable irreversibility within the cycle. Also, the so-called null-recurrence property of the cumulative efficiency of energy conversion over many cycles and the irreversible property of isolated, purely mechanical processes under external `macroscopic' operations are discussed in relation to the impossibility of a perpetual machine, or Maxwell's demon.