Stochastic Energetics of Non-uniform Temperature Systems
Miki Matsuo, Shin-ichi Sasa
TL;DR
This paper develops an energetic framework for Langevin systems with spatially varying temperature, resolving stochastic calculus ambiguities and analyzing thermodynamic efficiency in specific examples.
Contribution
It introduces a new energetic interpretation for non-uniform temperature stochastic systems, avoiding Itô-Stratonovich issues through a Kramers-based approach.
Findings
Defined heat consistently for non-uniform temperature systems
Analyzed the Thomson effect within this framework
Demonstrated a Brownian motor achieving Carnot efficiency
Abstract
We propose an energetic interpretation ofstochastic processes described by Langevin equations with non-uniform temperature. In order to avoid It\^{o}-Stratonovich dilemma, we start with a Kramers equation, and derive a Fokker-Plank equation by the renormalization group method. We give a proper definition of heat for the system. Based on our formulations,we analyze two examples, the Thomson effect and a Brownian motor which realizes the Carnot efficiency.
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Taxonomy
TopicsAdvanced Thermodynamics and Statistical Mechanics · stochastic dynamics and bifurcation · Ecosystem dynamics and resilience