English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We discuss and analyze the properties of Casimir forces acting betweennonreciprocal objects in thermal equilibrium. By starting from thefluctuation-dissipation theorem and splitting the force into those arising fromindividual sources, we show that if all temperatures are equal, the resultingforce is reciprocal and is derivable as the gradient of a Casimir (free)energy. While the expression for the free energy is identical to the one forreciprocal objects, there are several distinct features: To leading order inreflections, the free energy can be decomposed as the sum of two terms, thefirst corresponding to two reciprocal objects, and the second corresponding totwo anti-reciprocal objects. The first term is negative and typically yieldsattraction, while the second can have either sign. For the case of two objectsthat are each other's mirror images, the second term is positive and yieldsrepulsion. The sum of terms can lead to overall repulsive forces, in agreementwith previous observations. Stable configurations, ruled out for reciprocalcases, appear possible for nonreciprocal objects. We show that for threeobjects, a three-body free energy exists, indicating that previously foundpersistent heat currents in situations of three objects cannot be used toproduce persistent torques.

Equilibrium forces on non-reciprocal materials