WordPress code to increment Published times by one second for each post when multiple posts are Published in one call. This is a work-around for https://core.trac.wordpress.org/ticket/8107

publish-posts-increment-times.php

<?php

add_action( 'transition_post_status', 'srf_publish_post_unique_date', 10, 3 );

function srf_publish_post_unique_date( $new_status, $old_status, $post ) {

    // only perform operation when post is
    // changing to a status of 'publish'
    // otherwise (abort)
    if ( 'publish' !== $new_status ) { return; }

    // temporarily remove action from hook
    // to prevent endless loop
    remove_action( 'transition_post_status', 'srf_publish_post_unique_date' );

    $post = srf_increment_post_time( $post );

    // store updated post information to db
    wp_update_post( $post );

    // restore temporarily removed action from hook
    add_action( 'transition_post_status', 'srf_publish_post_unique_date', 10, 3 );
}

function srf_increment_post_time($post) {
    // track increment between calls
    global $srf_post_time_increment; 
    if ( !isset( $srf_post_time_increment ) ) { 
        // first call requires no increment
        // next call will increment by 1 sec
        $srf_post_time_increment = 1; 
        return $post;
    }

    // retrieve time and increment
    $gmt_time = strtotime( $post->post_date_gmt . ' GMT' );
    // increment by 1 sec each time this function is called 
    $gmt_time += $srf_post_time_increment;

    // update post object information
    $post->post_date_gmt = date( 'Y-m-d H:i:s', $gmt_time );
    $post->post_date = date( 'Y-m-d H:i:s', $gmt_time + ( get_option( 'gmt_offset') * HOUR_IN_SECONDS ) );

    // increment the counter for next call
    $srf_post_time_increment++;

    return $post; 
}