How to test time dependent code in Java? [czystykod.pl]

Task.java

public class Task {
    public String getAction() {...}
    public LocalDateTime getDueDate() {...}
    
    public boolean isOverdue(Clock clock) {
        return LocalDateTime.now(clock).isAfter(getDueDate());
    }
}

TaskSpec.groovy

class TaskSpec {
    Clock fixedClock = Clock.fixed(Instant.now()), ZoneId.systemDefault());

    def "task should become overdue when its' due date has come"() {
        given:
            LocalDateTime nowPlus10Seconds = LocalDateTime.now(fixedClock).plusSeconds(10);
            Task task = Tasks.withDueDate(nowPlus10Seconds, "Call to Venkat")

        expect:
            task.isOverdue(fixedClock) == false
            task.isOverdue(Clock.offset(fixedClock, Duration.ofSeconds(10))) == true
    }
}

WrongTask.java

// DON'T DO THIS
public class WrongTask {
    public String getAction() {...}
    public Date getDueDate() {...}
    
    public boolean isOverdue() {
        return System.currentTimeMillis() > getDueDate().getMillis();
    }
}

WrongTaskSpec.groovy

// DON'T DO THIS
class WrongTaskSpec {

    def "task should become overdue when its' due date has come"() {
        given:
            Date nowPlus10Seconds = new Date(System.currentTimeMillis() + TEN_SECONDS_AS_MS)
            Task task = Tasks.withDueDate(nowPlus10Seconds, "Call to Venkat")

        expect:
            task.isOverdue() == false
            TimeUnit.SECONDS.sleep(10)
            task.isOverdue() == true
    }
}