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With inspiration from other libraries

There is a newer version: 2.12.15

/**
 * Logback: the reliable, generic, fast and flexible logging framework.
 * Copyright (C) 1999-2015, QOS.ch. All rights reserved.
 *
 * This program and the accompanying materials are dual-licensed under
 * either the terms of the Eclipse Public License v1.0 as published by
 * the Eclipse Foundation
 *
 *   or (per the licensee's choosing)
 *
 * under the terms of the GNU Lesser General Public License version 2.1
 * as published by the Free Software Foundation.
 */
package ch.qos.logback.classic.pattern;

import ch.qos.logback.classic.spi.ILoggingEvent;

public class RelativeTimeConverter extends ClassicConverter {

    long lastTimestamp = -1;
    String timesmapCache = null;

    public String convert(ILoggingEvent event) {
        long now = event.getTimeStamp();

        synchronized (this) {
            // update timesmapStrCache only if now != lastTimestamp
            if (now != lastTimestamp) {
                lastTimestamp = now;
                timesmapCache = Long.toString(now - event.getLoggerContextVO().getBirthTime());
            }
            return timesmapCache;
        }
    }
}